GIFT   OF 
MICHAEL  REESE 


A  TEXT-BOOK 


OF 


MECHANICAL    DRAWING 


AND 

ELEMENTARY 


MACHINE   DESIGN 


BY 


JOHN    S.    REID, 

Instructor  in  Mechanical  Drawing  and  Designing, 

Sibley  College,  Cornell  University; 
Member  of  the  American  Society  of  Mechanical  Engineers; 

AND 

DAVID    REID, 

Instructor  in  Mechanical  Drawing  and  Designing, 

Sibley  College.  Cornell  University, 

Ithaca,  N.  Y. 


FIRST  EDITION. 
FIRST    THOUSAND. 


NEW  YORK: 

JOHN    WILEY   &   SONS. 

LONDON  :    CHAPMAN  &  HALL,  LIMITED. 

1901. 


Copyright,  1900, 

BY 
JOHN   S.  AND  DAVID   REID. 


ROBERT    DRUMMOND,    FRINTER,    NEW   YORK, 


PREFACE. 


To  properly  prepare  students  for  advanced  machine 
design  it  has  been  found  necessary  to  introduce  a  course 
designed  to  apply  the  principles  of  mechanical  drawing  to  the 
solution  of  practical  problems  in  machine  construction  and  to 
familiarize  the  student  with  the  arrangement  and  proportions 
of  the  most  important  machines  and  their  details  recognized 
by  competent  engineers  to  be  the  best  practice  of  the  present 
time. 

It  is  essential  to  intelligent  study  and  an  economical 
expenditure  of  time  and  labor  that,  before  attempting  to 
design  a  new  machine  or  improve  an  old  one,  the  student 
should  post  himself  with  all  possible  information  concerning 
what  has  already  been  done  in  the  same  direction. 

To  this  end  the  present  work  has  been  prepared.  In  it 
we  have  attempted  to  show  what  is  the  best  United  States 
practice  in  the  design  and  construction  of  various  machines 
and  details  of  machines,  using  rules  and  formulae  whenever 
feasible  in  working  out  practical  problems. 

In  addition  to  this  will  be  found  the  latest  and  most 
approved  drafting-room  methods  in  use  in  this  country,  with- 
out which  most  drawings  would  be  practically  useless.  Up 

to  the  present  time  no  text-book  that  we  know  of  has  been 

iii 


92424 


IV  PREFA  CE, 

published  in  the  United  States  that  could  in  the  best  way  fill 
the  need  as  explained  above. 

Books  of  a  somewhat  similar  nature  have  been  published 
in  Great  Britain,  showing  that  the  same  need  has  been  felt 
there  as  here.  These  books,  modified  to  suit  American  prac- 
tice, have  been  used  to  some  extent  in  this  country  because 
they  were  the  best  to  be  had,  but  are  not  by  any  means  all 
that  can  be  desired  for  our  purpose  in  their  present  form. 

While  preparing  this  course  for  the  sophomore  students  in 
Sibley  College  the  authors  endeavored  to  secure  samples  of 
the  actual  machines  or  parts  of  machines  as  collateral  in  illus- 
trating the  exercises  given  in  the  book,  with  a  result  that  in 
our  drafting-rooms  we  have  many  examples  of  modern 
machine  construction  placed  convenient  to  the  students' 
hands,  so  that  they  may  examine  and  handle  the  actual  tiling 
itself  while  solving  the  problems  in  drawing  and  designing. 
This  we  believe  of  great  importance  in  the  study  of  machine 
design  and  construction,  because  few  are  able  to  describe  a 
machine  even  with  the  assistance  of  a  drawing  so  well  as  to 
enable  the  student  to  conceive  it  in  his  mind  as  it  actually  is. 

The  preparation  necessary  for  the  proper  understanding 
and  execution  of  the  problems  contained  in  this  book  is  as 
follows:  use  of  instruments,  instrumental  drawings  applied  to 
drawing  geometrical  problems  in  pencil  and  ink,  thorough 
knowledge  of  the  conventional  lines,  hatch-lining  and  colors 
for  sections,  mechanical  and  free-hand  lettering,  orthographic 
projection  in  the  third  angle,  isometrical  drawing — in  brief  all 
.that  is  contained  in  "A  Course  in  Mechanical  Drawing,"  by 
John  S.  Reid,  published  by  John  Wiley  &  Sons,  New  York. 

In  the  preparation  of  the  drawings  for  this  work  we  are 


PREFA  CE.  V 

indebted  to  many  of  the  leading  engineering  firms  of  this  and 
other  States,  who  have  kindly  supplied  us  with  drawings  and 
samples  of  the  latest  and  best  practice  of  the  day.  Our 
thanks  are  especially  due  to  the  Dodge  Manufacturing  Com- 
pany, the  Detroit  Screw  Works,  the  Buckeye  Engine  Co., 
the  United  States  Metallic  Packing  Co.,  the  National  Tube 
Works,  the  Ridgeway  Dynamo  &  Engine  Co.,  the  Murray 
Gun  Works,  Henry  R.  Worthington,  Robt.  Pool  £  Sons, 
the  Baldwin  Locomotive  Works,  the  Schenectady  Locomotive 
Works,  the  American  Pulley  Co.,  the  Hyatt  Roller  Bearing 
Co.,  the  Macintosh  and  Seymour  Engine  Co.,  and  many 
others. 

Our  acknowledgments  are  also  due  to  many  of  the  best 
authorities  on  the  different  subjects  treated,  among  which 
may  be  mentioned  Thurston's  "  Materials  of  Construction," 
A.  W.  Smith's  "Machine  Design,"  Klein's  "  Machine 
Design,"  Unwin's  "  Machine  Design,"  Barr's  "  Boilers  and 
Furnaces,"  Peabody  and  Miller's  "  Steam  Boilers,"  Low 
and  Bevis's  "  Drawing  and  Designing,"  John  H.  Barr's 
"  Kinematics,"  Thurston's  "  Steam  Boilers,"  Reuleaux's 
"  Constructor,"  the  "  Proceedings  of  the  American  Railway 
Master  Mechanics'  Association,"  etc.,  etc. 

J.  S.  R. 

D.  R. 


CONTENTS. 


INTRODUCTORY   INSTRUCTIONS. 
J.  S.  R. 

PACK 

MECHANICAL  DRAWING i 

COMPLETE  OUTFIT 2 

USE  OF  INSTRUMENTS 7 

SHADE-LINES  AND  SHADING 15 

WORKING  DRAWINGS 17 

LETTERING 19 

FIGURING 19 

STANDARD  CONVENTIONS 20 

CROSS-SECTIONS 26 

CONSTRUCTIONS 26 

ELEMENTARY  MACHINE  DESIGN 29 

MATERIALS  OF  CONSTRUCTION 30 

STRENGTH  OF  MATERIALS 36 

USEFUL  TABLES,  ETC. 41 

CHAPTER  I. 
D.  R. 

SCREWS,  NUTS.  AND  BOLTS 48 

CHAPTER  II. 

D.  R. 

KEYS,  COTTERS,  AND  GIBS 109 

CHAPTER   III. 
J.  S.  R. 

RIVETS  AND  RIVETED  JOINTS .- 125 

CHAPTER   IV. 
J.  S.  R. 

SHAFTING  AND  SHAFT-COUPLINGS 157 

vii 


Vlll  CONTENTS. 


CHAPTER  V. 
J.  S.  R. 

PAGB 

PIPES  AND  PIPE-COUPLINGS 189 

CHAPTER  VI. 
D.  R. 

BEARINGS,  SOLE-PLATES,  AND  WALL  BOX-FRAMES 206 

CHAPTER  VII. 

I.  S.  R. 
BELT  GEARING 238 

CHAPTER  VIII. 

J.  S.  R. 

TOOTHED  GEARING 262 

CHAPTER  IX. 

J.  S.R. 
VALVES,  COCKS,  AND  OIL-CUPS 27$ 

CHAPTER  X. 
J.  S.  R.  &  D.  R. 

ENGINE  DETAILS 305, 


SUGGESTED    COURSES. 

FALL   TERM. 

1.  Ex.  i,  3,  4,  5,  6,  7,  10,  12,  13,  15,   19,  22,  24,  26,  29,  30,  32,  34,  38,  40, 

46,  Si- 

2.  Ex.   2,  3,  4,  5,  6,  8,  10,  n,  14,  16,  18,  20,  24,  27,  29,  31,  33,  35,  39,  41, 

47,  Si- 

3.  Ex.  i,  3,  4,   5,  6,  8,  9,  12,  13,  17,  19,  22,  23,  25,  29,  30,  32,  34,  38,  42, 

48,  5i. 

4.  Ex.  2,  3,  4,  5,  6,  7,  9,  ",  M,   15,  18.  21,  24,  28,  29,  31,  33,  36,  38,  43, 

49,  51. 

5.  Ex.  i,  3,  4,  5,  6,  8,  10,  12,  13,  16,  19,  22,  23,  26,  29,  30,  32,  34,  38,  44, 

50,  52. 

6.  Ex.  2,  3,  4,  5,  6,  7,  9,  u,  14,  17,  18,  21,  24,  27,  29,  31,  33,  37,  39,  45, 
50,  52. 

FALL  TERM  CONTINUED. 

1.  Ex.  52,  54,  59,  64,  68,  73,  77,  86,  89,  90,  93. 

2.  Ex.  52,  55,  60,  65,  70,  74,  84,  87,  90,  92,  94. 

3.  Ex.  52,  54,  61,  66,  71,  75,  85,  88,  90,  91,  93. 

4.  Ex.  52,  56,  62,  67,  70,  76,  84,  86,  90,  92,  94. 

5.  Ex.  53,  57,  63,  68,  71,  77,  85,  87,  90,  91,  93. 

6.  Ex.  53,  58,  64,  69,  72,  76,  84,  88,  90,  92,  94. 

WINTER    TERM. 

1.  Ex.  95,  97,  99,   lor,   103,   106,   108,   in,   113,  117,  119,   121,   124,   130, 

136,  139,  142,  145,  147,  149- 

2.  Ex.    96,    98,    100,    102,    104,     105,    107,    112,    114,    Il8,    120,    122,    125,    13*1 

137,  140,  143,  146,  148,  149. 

3.  Ex.  95,  97,  99.   loi,    104,    107,    no,  112,    115,  117,  121,  123,  126,   132, 

138,  139,  142,  145,  147,  140. 

4.  Ex.  96,  98,  100,   102,   103,  106,  108,  in,  113,    116,   119,    122,   127,  133, 

136,  138,  144,  146,  148,  149. 

5.  Ex.  95,  97,  99,   101,  104,   105,  108,    in,   113,  116,  120,  121,  128,  134, 

137,  140,  142,  145,  147,  149. 

6.  Ex.  96,  98,  loo,  102,   106,   107,   no,  112,   115,   117,  119,  122,  129,  135, 
136.  138,  143,  146,  148,  149. 


DRAWING  AND   DESIGNING 


INTRODUCTORY    INSTRUCTIONS. 

MECHANICAL  drawing  as  applied  to  machine  drawing  and 
design  consists  of  the  application  of  descriptive  geometry  or 
orthographic  projection  to  the  delineation  of  machines  and 
parts  of  machines  (modified  sometimes  by  certain  conven- 
tions) generally  recognized  by  experienced  draftsmen. 

It  is  comparatively  a  simple  matter  for  any  person  of 
average  intelligence  to  acquire  the  ability  of  making  a  fairly 
accurate  mechanical  drawing  of  a  machine,  given  the  dimen- 
sions, but  it  is  altogether  a  different  and  more  difficult  prob- 
lem to  determine  those  dimensions  that  will  give  the  best 
form  and  proportion  to  the  different  parts  of  the  machine  as 
will  enable  them  to  properly  perform  the  functions  for  which 
they  are  intended  in  accordance  with  the  strength  of  the 
material  of  which  they  may  be  made. 

A  mere  copy  of  a  drawing  unaccompanied  by  some  means 
for  compelling  the  student  to  study  (i)  the  form  and  propor- 
tions given  and  reasons  for  same  or  (2)  the  illustrations  of 
some  principle  connected  with  projection  is  not  of  much 
moment  in  the  study  of  machine  drawing  and  design.  But  a 
problem  in  drawing  and  design  illustrated  by  a  drawing  of 
the  object,  representing  the  best  modern  practice  and  requir- 
ing the  calculation  of  the  proportions  of  the  different  parts 


2  DRAWING   AND   DESIGNING. 

from  rules  and  formulae,  will  induce  the  student  to  think,  and 
tend  to  develop  any  natural  ability  he  may  have  in  this  direc- 
tion. It  has  been  the  aim  of  the  authors  in  the  arrangement 
of  problems  to  accomplish  this  purpose  in  the  highest  degree 
possible. 

The  following  notes  on  the  complete  outfit  of  instruments 
and  materials  should  be  consulted  before  buying,  because  it 
is  very  essential  to  the  best  results  that  a  good  outfit  be 
secured. 

The  complete  outfit  for  students  in  mechanical  drawing  in 
Sibley  College  is  as  follows : 

(1)  THE  DRAWING-BOARD  for  freshman  work  is  if  x  22'*' 
X  -£",  the  same  as  that   used   for  free-hand    drawing.     The 
board  for  sophomore  and  junior  drawing  is  20"  X  26"  X  not 
more  than  J-"  in  thickness.      The  material  should  be  soft  pine 
and  constructed  as  shown  by  Fig.  I. 

(2)  PAPER,  Paragon,  eggshell  surface,  size  18"  X  24". 

(3)  PENCILS,  one  6H  and  one  4H   Koh-i-noor  or  Faber, 
also  one  Eagle  Pilot  No.  2  with  rubber  tip. 

(4)  The  T-SQUARE  for  freshman  work  is  furnished  by  the 

department ;  a  plain  pear- 
wood  T-square  with  a 
fixed  head  is  all  that  is 
necessary  for  sophomore 
or  junior  work.  Length 
to  suit  drawing-board. 
(5)  INSTRUMENTS. — 

r  IG.   I. 

The       "  Sibley       College 

Set,"  shown  by  Fig.  2,  is  recommended  as  a  first-class 
medium-priced  set  of  instruments.  It  contains: 


IN  TROD  UCTOR  Y  INSTR  UCTIONS. 


FIG.  2. 


A  COMPASS,  5^"  long,  with 
fixed  needle-point,  pencil,  pen, 
and  lengthening  bar. 

A  SPRING  Bow  PENCIL, 
3"  long. 

A  SPRING  Bow  PEN,  3" 
long. 

A  SPRING  Bow  SPACER,  3 
long. 

A  DRAWING-PEN,  medium  length. 

A  HAIR-SPRING  DIVIDER,  5"  long. 

A  nickel-plated  box  with  leads. 

(6)  A  TRIANGULAR  BOXWOOD  SCALE  graduated  as  fol- 


\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\^\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\  \\\\\\\\\\\\\\\\\\  \V\\\\\\\\\\\\\\V 

FIG.  3. 

lows  :  4"  and  2",  3"  and  i  J",  i"  and  i"t  f"  andf ",  TY'  and 


FIG.  4. 


DRAWING   AND    DESIGNING. 


(7)  i  TRIANGLE  30°  x  60°,  celluloid,  10"  long. 

i         "          45°,  "  7"     " 

(8)  "SiBLEY  COLLEGE  SET"  of  IRREGULAR  CURVES. 


FIG.  5. 

(9)  GLASS-PAPER  PENCIL  SHARPENER. 


FIG.  6. 


(10)  INK,  black  waterproof,  S.&H.      Fig.  7. 
00     "      red  -  Higgins.      Fig.  8, 

(12)     "      blue 


FIG.  7. 


FIG.  8. 


INTRODUCTORY  INSTRUCTIONS.  5 

(13)  INK  ERASER,  Faber's  Typewriter. 

(14)  PENCIL  ERASER,  Tower's  Multiplex  Rubber.    Fig.  9. 

(15)  SPONGE   RUBBER   or  FABER'S  KNEADED  RUBBER. 
Fig.   10. 


FIG.  9. 

(16)  TACKS,  a  small  box  of  I  oz.  tacks. 

(17)  WATER-COLORS,  J  pan  each  of  Payne's  Gray,  Crim- 
son Lake,  Prussian  Blue,  Burnt  Sienna,  and  Gamboge.    Wind- 
sor &  Newton.      Fig.  ii. 


FIG.  10.  FIG.  ii. 

(18)  TINTING  BRUSH,  Camel's  Hair  No.  10.     Fig.  12, 


FIG.  12. 


(19)  TINTING  SAUCER.     Fig.  13. 

(20)  WATER  GLASS.     Fig.  14. 

(21)  ARKANSAS  OIL-STONE.     2"x  \" 


6  DRA  WING  AND  DESIGNING. 

(22)  PIECE  OF  SHEET  CELLULOID,  color  No.  300,  thick- 
ness  T7roiF>  dull  on  b°tn  sides. 

(23)  PROTRACTOR,  German  silver,  about  5 ''diam.   Fig.  15, 

(24)  SCALE  GUARD,     •'         "        Fig.  16. 


FIG.  13.  FIG.  14. 

(25)  SHEET  OF  TRACING-CLOTH,  18"  x  24". 

(26)  WRITING-PEN,  point,  "Gillott"  No.  303. 


FIG.  15.  FIG.  16. 


(27)  Piece  of  SHEET  BRASS,  4"X4". 

(28)  NEEDLES,  two  with  handles. 

The  following  numbers  of  "  The  Complete  Outfit  "  are 
all  that  the  student  will  be  required  to  purchase  for  freshman 
mechanical  drawing :  2,  3,  5,  6,  7,  8,  9,  10,  13,  14,  16,  26. 

The  remainder  of  the  outfit  may  be  purchased  during  the 
sophomore  and  junior  years. 


IN  TROD  UCTOR  Y  INS  TR  UCTIONS. 


INSTRUMENTS. 

IT  is  a  common  belief  among  students  that  any  kind  of 
cheap  instrument  will  do  with  which  to  learn  mechanical 
drawing,  and  not  until  they  have  acquired  the  proper  use  of 
the  instruments  should  they  spend  money  in  buying  a  first- 
class  set.  This  is  one  of  the  greatest  mistakes  that  can  be 
made.  Many  a  student  has  been  discouraged  and  disgusted 
because,  try  as  he  would,  he  could  not  make  a  good  drawing, 
using  a  set  of  instruments  with  which  it  would  be  difficult  for 
even  an  experienced  draftsman  to  make  a  creditable  showing. 

If  it  is  necessary  to  economize  in  this  direction  it  is  better 
and  easier  to  get  along  with  a  fewer  number,  and  have  them 
of  the  best,  than  it  is  to  have  an  elaborate  outfit  of  question- 
able quality. 

The  instruments  composing  the  "Sibley  College  Set" 
are  made  by  T.  Alteneder  &  Sons,  and  are  certainly  as  good 
as  the  best.  See  Fig.  17. 

USE    OF    INSTRUMENTS. 

The  Pencil. — Designs  of  all  kinds  are  usually  worked  out 
in  pencil  first,  and  if  to  be  finished  and  kept  they  are  inked  in 
and  sometimes  colored  and  shaded ;  but  if  the  drawing  is  only 
to  be  finished  in  pencil,  then  all  the  lines  except  construction, 
center,  and  dimension  lines  should  be  made  broad  and  dark, 


DRA  WING  AND  DESIGNING. 

so  that  the  drawing  will  stand  out  clear  and  distinct.  It  will 
be  noticed  that  this  calls  for  two  kinds  of  pencil-lines,  the 
first  a  thin,  even  line  made  with  a  hard,  fine-grained  lead- 
pencil,  not  less  than  6H  (either  Koh-i-noor  or  Faber's),  and 
sharpened  to  a  knife-edge  in  the  following  manner :  The  lead 
should  be  carefully  bared  of  the  wood  with  a  knife  for  about 
|-",  and  the  wood  neatly  tapered  back  from  that  point;  then 
lay  the  lead  upon  the  glass-paper  sharpener  illustrated  in  the 
outfit,  and  carefully  rub  to  and  fro  until  the  pencil  assumes  a 
long  taper  from  the  wood  to  the  point ;  now  turn  it  over  and 
do  the  same  with  the  other  side,  using  toward  the  last  a 
slightly  oscillating  motion  on  both  sides  until  the  point  has 
assumed  a  sharp,  thin,  knife-edge  endwise  and  an  elliptical 
contqur  the  other  way. 

This  point  should  then  be  polished  on  a  piece  of  scrap 
drawing-paper  until  the  rough  burr  left  by  the  glass-paper  is 
removed,  leaving  a  smooth,  keen,  ideal  pencil-point  for  draw- 
ing straight  lines. 

With  such  a  point  but  little  pressure  is  required  in  the 
hands  of  the  draftsman  to  draw  the  most  desirable  line,  one 
that  can  be  easily  erased  when  necessary  and  inked  in  to 
much  better  advantage  than  if  the  line  had  been  made  with  a 
blunt  point,  because,  when  the  pencil-point  is  blunt  the  incli- 
nation is  to  press  hard  upon  it  when  drawing  a  line.  This 
forms  a  groove  in  the  paper  which  makes  it  very  difficult  to 
draw  an  even  inked  line. 

The  second  kind  of  a  pencil-line  is  the  broad  line,  as 
explained  above ;  it  should  be  drawn  with  a  somewhat  softer 
pencil,  say  4H,  and  a  thicker  point. 

All  lines  not  necessary  to  explain  the  drawing  should  be. 


IN  TROD  UCTOK  Y  INS  TR  UCTIONS. 


9 


erased  before  inking  or  broadening  the  pencil-lines,  so  as  to 
make  a  minimum  of  erasing  and  cleaning  after  the  drawing  is 
finished. 

When  drawing  pencil-lines,  the  pencil  should  be  held  in  a 
plane  passing  through  the  edge  of  the  T-square  perpen- 
dicular to  the  plane  of  the  paper  and  making  an  angle  with 
the  plane  of  the  paper  equal  to  about  60°. 

Lines  should  always  be  drawn  from  left  to  right.  A  soft 
conical-pointed  pencil  should  be  used  for  lettering,  figuring, 
and  all  free-hand  work. 

The  Drawing-pen. — The  best  form,  in  the  writer's  opinion, 
is  that  shown  in  Fig.  17.  The  spring  on  the  upper  blade 


FIG.  17. 

spreads  the  blades  sufficiently  apart  to  allow  for  thorough 
cleaning  and  sharpening.  The  hinged  blade  is  therefore 
unnecessary.  The  pen  should  be  held  in  a  plane  passing 
through  the  edge  of  the  T-square  at  right  angles  to  the  plane 
of  the  paper,  and  making  an  angle  with  the  plane  of  the 
paper  ranging  from  60°  to  90°. 

The  best   of  drawing-pens  will  in  time  wear  dull  on  the 
point,  and   until  the  student  has  learned  from  a  competent 


IO  DRA  WING  AND  DESIGNING. 

teacher  how  to  sharpen  his  pens  it  would  be  better  to  have 
them  sharpened  by  the  manufacturer. 

It  is  difficult  to  explain  the  method  of  sharpening  a  draw- 
ing-pen. 

If  one  blade  has  worn  shorter  than  the  other,  the  blades 
should  be  brought  together  by  means  of  the  thumb-screw,  and 
placing  the  pen  in  an  upright  position  draw  the  point  to  and 
fro  on  the  oil-stone  in  a  plane  perpendicular  to  it,  raising  and 
lowering  the  handle  of  the  pen  at  the  same  time,  to  give  the 
proper  curve  to  the  point.  The  Arkansas  oil-stones  (No.  2  I 
of  "  The  Complete  Outfit  ")  are  best  for  this  purpose. 

The  blades  should  next  be  opened  slightly,  and  holding 
the  pen  in  the  right  hand  in  a  nearly  horizontal  position,  place 
the  lower  blade  on  the  stone  and  move  it  quickly  to  and  fro, 
slightly  turning  the  pen  with  the  fingers  and  elevating  the 
handle  a  little  at  the  end  of  each  stroke.  Having  ground  the 
lower  blade  a  little,  turn  the  pen  completely  over  and  grind 
the  upper  blade  in  a  similar  manner  for  about  the  same  length 
of  time ;  then  clean  the  blades  and  examine  the  extreme 
points,  and  if  there  are  still  bright  spots  to  be  seen  continue 
the  grinding  until  they  entirely  disappear,  and  finish  the 
sharpening  by  polishing  on  a  piece  of  smooth  leather. 

The  blades  should  not  be  too  sharp,  or  they  will  cut  the 
paper.  The  grinding  should  be  continued  only  as  long  as  the 
bright  spots  show  on  the  points  of  the  blades. 

When  inking,  the  pen  should  be  held  in  about  the  same 
position  as  described  for  holding  the  pencil.  Many  drafts- 
men hold  the  pen  vertically.  The  position  may  be  varied 
with  good  results  as  the  pen  wears.  Lines  made  with  the 
pen  should  only  be  drawn  from  left  to  right. 


INTRODUCTORY  INSTRUCTIONS.  II 

THE   TRIANGLES. 

The  triangles  shown  at  Fig.  4  (in  "  The  Complete  Outfit ") 
are  10"  and  rj"  long  respectively,  and  are  made  of  transparent 
celluloid.  The  black  rubber  triangles  sometimes  used  are  but 
very  little  cheaper  (about  10  cents)  and  soon  become  dirty 
when  in  use ;  the  rubber  is  brittle  and  more  easily  broken  than 
the  celluloid. 

Angles  of  15°,  75°,  30°,  45°,  60°,  and  90°  can  readily  be 
drawn  with  the  triangles  and  T-square.  Lines  parallel  to 
oblique  lines  on  the  drawing  can  be  drawn  with  the  triangles 
by  placing  the  edge  representing  the  height  of  one  of  them 
so  as  to  coincide  with  the  given  line,  then  place  the  edge  rep- 
resenting the  hypotenuse  of  the  other  against  the  corre- 
sponding edge  of  the  first,  and  by  sliding  the  upper  on  the 
lower  when  holding  the  lower  firmly  with  the  left  hand  any 
number  of  lines  may  be  drawn  parallel  to  the  given  line. 

The  methods  of  drawing  perpendicular  lines  and  making 
angles  with  other  lines  within  the  scope  of  the  triangles  and  T- 
square  are  so  evident  that  further  explanation  is  unnecessary. 

THE    T-SQUARE. 

The  use  of  the  T-square  is  very  simple,  and  is  accom- 
plished by  holding  the  head  firmly  with  the  left  hand  against 
the  left-hand  end  of  the  drawing-board,  leaving  the  right 
hand  free  to  use  the  pen  or  pencil  in  drawing  the  required 
lines. 

THE   DRAWING-BOARD. 

If  the  left-hand  edge  of  the  drawing-board  is  straight  and 


12  DRAWING  AND  DESIGNING. 

the  T-squarc,  then  horizontal  lines  parallel  to  the  upper  edge* 
of  the  paper  and  perpendicular  to  the  left-hand  edge  may  be 
drawn  with   the   T-square,  and   lines   perpendicular  to  these 
can  be  made  by  means  of  the  triangles,  or  set  squares,  as  they 
are  sometimes  called. 

THE    SIBLEY    COLLEGE    SCALE. 

This  scale,  illustrated  in  Fig.  3  (in  "  The  Complete  Out- 
fit"), was  arranged  to  suit  the  needs  of  the  students  in  Sibley 
College.  It  is  triangular  and  made  of  boxwood.  The  six 
edges  are  graduated  as  follows;  TV'  or  full  size,  -g^",  1" 
and  f"  =  I  ft.,  i"  and  i"  =  i  ft.,  3"  and  \\"  =  I  ft.,  and 
4"  and  2"  =  I  ft. 

Drawings  of  very  small  objects  are  generally  shown  en- 
larged— e.g.,  if  it  is  determined  to  make  a  drawing  twice  the 
full  size  of  an  object,  then  where  the  object  measures  one  inch 
the  drawing  would  be  made  2" ,  etc. 

Larger  objects  or  small  machine  parts  are  often  drawn  full 
size — i.e.,  the  same  size  as  the  object  really  is — and  the  draw- 
ing is  said  to  be  made  to  the  scale  of  full  size. 

Large  machines  and  large  details  are  usually  made  to  a 
reduced  scale — e.g.,  if  a  drawing  is  to  be  made  to  the  scale  of 
2"  —  i  ft.,  then  2"  measured  by  the  standard  rule  would  be 
divided  into  12  equal  parts  and  each  part  would  represent  i" ' . 


THE    SCALE    GUARD. 

This  instrument  is  shown  in  Fig.  16  (in  "The  Complete 
Outfit ").  It  is  employed  to  prevent  the  scale  from  turning, 
so  that  the  draftsman  can  use  it  without  having  to  look  for 


INTRODUCTORY  INSTRUCTIONS.  1 3 

the  particular  edge  he  needs  every  time  he  wants  to  lay  off 
a  measurement. 

THE    COMPASSES. 

When  about  to  draw  a  circle  or  an  arc  of  a  circle,  take 
hold  of  the  compass  at  the  joint  with  the  thumb  and  two  first 
fingers,  guide  the  needle-point  into  the  center  and  set  the 
pencil  or  pen  leg  to  the  required  radius,  then  move  the  thumb 
and  forefinger  up  to  the  small  handle  provided  at  the  top  of 
the  instrument,  and  beginning  at  the  lowest  point  draw  the 
line  clockwise.  The  weight  of  the  compass  will  be  the  only 
down  pressure  required. 

The  sharpening  of  the  lead  for  the  compasses  is  a  very  im- 
portant matter,  and  cannot  be  emphasized  too  much.  Before 
commencing  a  drawing  it  pays  well  to  take  time  to  properly 
sharpen  the  pencil  and  the  lead  for  compasses  and  to  keep 
them  always  in  good  condition. 

The  directions  for  sharpening  the  compass  leads  are  the 
same  as  has  already  been  given  for  the  sharpening  of  the 
straight-line  pencil. 

• 
THE   DIVIDERS    OR    SPACERS. 

This  instrument  should  be  held  in  the  same  manner  as  de- 
scribed for  the  compass.  It  is  very  useful  in  laying  off  equal 
distances  on  straight  lines  or  circles.  To  divide  a  given  line 
into  any  number  of  equal  parts  with  the  dividers,  say  12,  it 
is  best  to  divide  the  line  into  three  or  four  parts  first,  say  4, 
and  then  when  one  of  these  parts  has  been  subdivided  accu- 
rately into  three  equal  parts,  it  will  be  a  simple  matter  to 
step  off  these  latter  divisions  on  the  remaining  three-fourths 


DRA  WING  AND  DESIGNING. 

of  the  given  line.  Care  should  be  taken  not  to  make  holes  in- 
the  paper  with  the  spacers,  as  it  is  difficult  to  ink  over  them 
without  blotting. 

THE    SPRING    BOWS. 

These  instruments  are  valuable  for  drawing  the  small  cir- 
cles and  arcs  of  circles.  It  is  very  important  that  all  the 
small  arcs,  such  as  fillets,  round  corners,  etc.,  should  be  care- 
fully pencilled  in  before  beginning  to  ink  a  drawing.  Many 
good  drawings  are  spoiled  because  of  the  bad  joints  between 
small  arcs  and  straight  lines. 

When  commencing  to  ink  a  drawing,  all  small  arcs  and 
small  circles  should  be  inked  first,  then  the  larger  arcs  and 
circles,  and  the  straight  lines  last.  This  is  best,  because  it  is 
much  easier  to  know  where  to  stop  the  arc  line,  and  to  draw 
the  straight  line  tangent  to  it,  than  vice  versa. 

IRREGULAR   CURVES. 

The  Sibley  College  Set  of  Irregular  Curves  shown  in  Fig. 
5  are  useful  for  drawing  irregular  curves  through  points  that 
have  already  been  found  by  construction,  such  as  ellipses, 
cycloids,  epicyloids,  etc.,  as  in  the  cases  of  gear-teeth,  cam 
outlines,  rotary  pump  wheels,  etc. 

When  using  these  curves,  that  curve  should  be  selected 
that  will  coincide  with  the  greatest  number  of  points  on  the 
line  required. 

THE  PROTRACTOR. 

This  instrument  is  for  measuring  and  constructing  angles. 
It  is  shown  in  Fig.  15.  It  is  used  as  follows  when  measuring 


INTRODUCTORY  INSTRUCTIONS.  1 5 

an  angle:  Place  the  lower  straight  edge  on  the  straight  line 
which  forms  one  of  the  sides  of  the  angle,  with  the  nick 
exactly  on  the  point  of  the  angle  to  be  measured.  Then  the 
number  of  degrees  contained  in  the  angle  may  be  read  from 
the  left,  clockwise. 

In  constructing  an  angle,  place  the  nick  at  the  point  from 
which  it  is  desired  to  draw  the  angle,  and  on  the  outer  circum- 
ference of  the  protractor,  find  the  figure  corresponding  to  the 
number  of  degrees  in  the  required  angle,  and  mark  a  point  on 
the  paper  as  close  as  possible  to  the  figure  on  the  protractor; 
after  removing  the  protractor,  draw  a  line  through  this  point 
to  the  nick,  which  will  give  the  required  angle. 

SHADE   LINES   AND    SHADING. 

Shade  Lines  are  quite  generally  used  on  engineering  work- 
ing drawings ;  they  give  a  relieving  appearance  to  the  projec- 
ting parts,  improve  the  looks  of  the  drawing  and  make  it  easier 
to  read,  and  are  quickly'  and  easily  applied. 

The  Shading  of  the  curved  surfaces  of  machine  parts  is 
sometimes  practiced  on  specially  finished  drawings,  but  on 
working  drawings  most  employers  will  not  allow  shading  be- 
cause it  takes  too  much  time,  and  is  not  essential  to  a  quick 
and  correct  reading  of  a  drawing,  especially  if  a  system  of 
shade  lines  is  used. 

The  Source  of  Light  is  considered  to  be  at  an  infinite  dis- 
tance from  the  object,  therefore  the  Rays  of  Light  will  be  rep- 
resented by  parallel  lines. 

The  Source  of  Light  is  considered  to  be  fixed,  and  the  Point 
of  Sight  situated  in  front  of  the  object  and  at  an  infinite  dis- 


i6 


DRAWING   AND   DESIGNING. 


tance  from  it,  so  that  the  Visual  Rays  are  parallel  to  one 
another  and  per.  to  the  plane  of  projection. 

Shade  Lines  divide  illuminated  surfaces  from  dark  surfaces. 

Dark  surfaces  are  not  necessarily  to  be  defined  by  those 
surfaces  which  are  darkened  by  the  shadow  cast  by  another 
part  of  the  object,  but  by  reason  of  their  location  in  relation 
to  the  rays  of  light. 

It  is  the  general  practice  to  shade-line  the  different  pro- 
jections of  an  object  as  if  each  projection  was  in  the  same 
plane — e.g.,  suppose  a  cube,  Fig.  18,  situated  in  space  in  the 
third  angle,  the  point  of  sight  in  front  of  it,  and  the  direction 


FIG.  18. 


FIG.  19. 


of  the  rays  of  light  coinciding  with  the  diagonal  of  the  cube, 
as  shown  by  Fig.  19.  Then  the  edges  a"bv,  bvc°  will  be  shade 
lines,  because  they  are  the  edges  which  separate  the  illumi- 
nated faces  (the  faces  upon  which  fall  the  rays  of  light)  from 
the  shaded  faces,  as  shown  by  Fig.  19. 

Now  the  source  of  light  being  fixed,  let  the  point  of  sight 


INTRODUCTORY  INSTRUCTIONS.  I/ 

remain  in  the  same  position,  and  conceive  the  object  to  be  re- 
volved through  the  angle  of  90°  about  a  hor.  axis  so  that  a 
plan  at  the  top  of  the  object  is  shown  above  the  elevation,  and! 
as  the  projected  rays  of  light  falling  in  the  direction  of  the 
diagonal  of  a  cube  make  angles  of  45°  with  the  hor.,  then  with 
the  use  of  the  45°  triangle  we  can  easily  determine  that  the 
lower  and  right-hand  edges  of  the  plan  as  well  as  of  the  ele- 
vation should  be  shade  lines. 

This  practice  then  will  be  followed  in  this  work,  viz. : 

Shade  lines  shall  be  applied  to  all  projections  of  an  object, 
considering  the  rays  of  light  to  fall  upon  each  of  them,  from 
the  same  direction. 

Shade  lines  should  have  a  width  equal  to  3  times  that  of 
the  other  outlines.  Broken  lines  should  never  be  shade  lines. 

The  outlines  of  surfaces  of  revolution  should  not  be  shade 
lines.  The  shade-lined  figures  which  follow  will  assist  in  il- 
lustrating the  above  principles ;  they  should  be  studied  until 
understood. 

WORKING   DRAWINGS. 

Working  drawings  are  sometimes  made  on  brown  detail- 
paper  in  pencil,  traced  on  tracing-paper  or  cloth,  and  then 
blue  printed. 

The  latter  process  is  accomplished  as  follows : 

The  tracing  is  placed  face  down  on  the  glass  in  the  print- 
ing-frame, and  the  prepared  paper  is  placed  behind  it,  with 
the  sensitized  surface  in  contact  with  the  back  of  the  tracing. 

In  printing  from  a  negative  the  sensitized  surface  of  the 
prepared  paper  is  placed  in  contact  with  the  film  side  of  the 
negative,  and  the  face  is  exposed  to  the  light. 


1 8  DRAWING  AND  DESIGNING. 

The  blue-print  system  for  working  drawings  has  many 
drawbacks,  e.g.,  the  sectional  parts  of  the  drawing  requires  to 
be  hatch-lined,  using  the  standard  conventions  already  re- 
ferred to  for  the  different  materials.  This  takes  a  great  deal 
of  time.  The  print  has  usually  to  be  mounted  on  cardboard, 
although  this  is  not  always  done,  and  unless  it  is  varnished 
the  frequent  handling  with  dirty,  oily  fingers  soon  makes  it 
unfit  for  use. 

Changes  can  be  made  on  the  prints  with  soda-water,  it  is 
true,  but  they  seldom  look  well,  and  when  many  changes  or 
additions  require  to  be  made  it  is  best  to  make  them  on  the 
tracing  and  take  a  new  print.  And  the  sunlight  is  not  always 
favorable  to  quick  printing.  So  taking  everything  into  con- 
sideration the  system  of  making  working  drawings  directly  on 
cards  and  varnishing  them  is  probably  the  best.  It  is  the 
system  used  by  the  Schenectady  Locomotive  Works  and 
many  other  large  engineering  establishments.  In  size  the 
cards  are  made  9"  X  12",  12"  X  18",  18"  X  24";  they  are 
made  of  thick  pasteboard  mounted  with  Irish  linen  record- 
paper.  The  drawings  are  pencilled  and  inked  on  these  cards 
in  the  usual  way,  and  the  sections  are  tinted  with  the  conven- 
tional colors,  which  are  much  quicker  applied  than  hatch- 
lines.  The  face  of  the  drawing  is  protected  with  two  coats  of 
white  shellac  varnish,  while  the  back  of  the  card  is  usually 
given  a  coat  of  orange  shellac. 

The  white  varnish  can  easily  be  removed  with  a  little 
alcohol,  and  changes  made  on  the  drawing,  and  when  revar- 
nished  it  is  again  ready  for  the  shop. 

In  the  hands  of  an  experienced  workman  a  working 
drawing  is  intended  to  convey  to  him  all  the  necessary 


INTRODUCTORY  INSTRUCTIONS.  19 

information  as  to  shape,  size,  material,,  and  finish  to  en- 
able him  to  properly  construct  it  without  any  additional  in- 
structions. This  means  that  it  must  have  a  sufficient  num- 
"  her  of  elevations,  sections,  and  plans  to  thoroughly  explain 
and  describe  the  object  in  every  particular.  And  these  views 
should  be  completely  and  conveniently  dimensioned.  The 
dimensions  on  the  drawing  must  of  course  give  the  sizes  to 
which  the  object  is  to  be  made,  without  reference  to  the  scale 
to  which  it  may  be  drawn.  The  title  of  a  working  drawing 
should  be  as  brief  as  possible,  and  not  very  large- — a  neat, 
plain,  free-hand  printed  letter  is  best  for  this  purpose. 

Finished  parts  are  usually  indicated  by  the  letter  "  f,"  and 
if  it  is  all  to  be  finished,  then  below  the  title  it  is  customary 
to  write  or  print  "  finished  all  over." 

The  number  of  the  drawing  may  be  placed  at  the  upper 
left-hand  corner,  and  the  initials  of  the  draftsman  immedi- 
ately below  it. 

Lettering. — All  lettering  on  mechanical  drawings  should 
be  plain  and  legible,  but  the  letters  in  a  title  or  the  figures 
on  a  drawing  should  never  be  so  large  as  to  make  them  ap- 
pear more  prominent  than  the  drawing  itself. 

The  best  form  of  letter  for  practical  use  is  that  which  gives 
the  neatest  appearance  with  a  maximum  of  legibility  and  re- 
quires the  least  amount  of  time  and  labor  in  its  construction. 

Figuring. — Great  care  should  be  taken  in  figuring  or  di- 
mensioning a  mechanical  drawing,  and  especially  a  working 
drawing. 

To  have  a  drawing  accurately,  legibly,  and  neatly  figured 
is  considered  by  practical  men  to  be  the  most  important  part 
of  a  working  drawing. 


20  DRA  WING  AND  DESIGNING. 

There  should  be»  absolutely  no  doubt  whatever  about  the 
character  of  a  number  representing  a  dimension  on  a  drawing. 

Many  mistakes  have  been  made,  incurring  loss  in  time, 
labor,  and  money  through  a  wrong  reading  of  a  dimension. 

Drawings  should  be  so  fully  dimensioned  that  there  will 
be  no  need  for  the  pattern-maker  or  machinist  to  measure  any 
part  of  them.  Indeed,  means  are  taken  to  prevent  him  from 
doing  so,  because  of  the  liability  of  the  workman  to  make 
mistakes,  so  drawings  are  often  made  to  scales  which  are  dif- 
ficult to  measure  with  a  common  rule,  such  as  2 ''and  4"  = 
I  ft. 

STANDARD    CONVENTIONAL   SECTION   LINES. 

Conventional  section  lines  are  placed  on  drawings  to  distin- 
guish the  different  kinds  ot  materials  used  when  such  drawings 
are  to  be  finished  in  pencil,  or  traced  for  blue  printing,  or  to 
be  used  for  a  reproduction  of  any  kind. 

Water-colors  are  nearly  always  used  for  finished  drawings 
and  sometimes  for  tracings  and  pencil  drawings. 

The  color  tints  can  be  applied  in  much  less  time  than  it 
takes  to  hatch-line  a  drawing.  So  that  the  color  method 
should  be  used  whenever  possible. 

To  apply  the  color  tint. — Great  care  should  be  taken  in  de- 
termining the  depth  of  the  tint  to  be  used ;  when  only  the 
section  parts  are  to  be  colored  the  tints  should  be  quite  light 
because  it  is  much  easier  to  obtain  an  even  wash  and  a  softer 
and  more  artistic  effect.  Before  applying  the  color  the  draw- 
ing board  should  be  cleared  of  drawing  instruments,  etc.,  so 
that  it  may  be  easily  turned  to  enable  the  student  to  keep 


INTRODUCTORY  INSTRUCTIONS.  21 

the  bounding  color  line  always  to  his  left,  and  keeping  the 
brush  in  such  position  that  the  color  just  touches  the  bound- 
ing line  transfer  the  color  to  the  drawing  with  long  sweeps  of 
the  brush  until  the  surface  is  covered.  Press  out  all  color 
remaining  in  the  brush  with  the  fingers  and  apply  the  brush 
again  to  the  little  puddles  remaining  on  the  paper.  The 
brush  will  draw  it  back  into  itself  and  leave  an  even  tint  all 
over  the  section. 

FiG.  20. — This  figure  shows  a  collection  of  hatch-lined 
sections  that  is  now  cue  almost  universal  practice  among 
draftsmen  in  this  and  other  countries,  and  may  be  considered 
standard. 

No.  i.  To  the  right  is  shown  a  section  of  a  wall  made  o£ 
rocks.  When  used  without  color,  as  in  tracing  for  printing, 
the  rocks  are  simply  shaded  with  India  ink  and  a  175  Gillott 
steel  pen.  For  a  colored  drawing  the  ground  work  is  made 
of  gamboge  or  burnt  umber.  To  the  left  is  the  conventional 
representation  of  water  for  tracings.  For  colored  drawings 
a  blended  wash  of  Prussian  blue  is  added. 

No.  2.  Convention  for  Marble. —  When  colored,  the 
whole  section  is  made  thoroughly  wet  and  each  stone  is  then 
streaked  with  Payne's  gray. 

No.  3.  Convention  for  Chestnut. —  When  colored,  a 
ground  wash  of  gamboge  with  a  little  crimson  lake  and  burnt 
umber  is  used.  The  colors  for  graining  should  be  mixed  in  a 
separate  dish,  burnt  umber  with  a  little  Payne's  gray  and 
crimson  lake  added  in  equal  quantities  and  made  dark  enough 
to  form  a  sufficient  contrast  to  the  ground  color. 

No.  4.  General  Convention  for  Wood. — When  colored  the 
ground  work  should  be  made  with  a  light  wash  of  burnt  sienna. 


22 


DRA  WING  AND  DESIGNING. 


INTRODUCTORY  INSTRUCTIONS.  2$ 

The  graining  should  be  done  with  a  writing-pen  and  a  dark 
mixture  of  burnt  sienna  and  a  modicum  of  India  ink. 

No.  5.  Convention  for  Black  Walnut. — A  mixture  of 
Payne's  gray,  burnt  umber  and  crimson  lake  in  equal  quanti- 
ties is  used  for  the  ground  color.  The  same  mixture  is  used 
for  graining  when  made  dark  by  adding  more  burnt  umber. 

No.  6.  Convention  for  Hard  Pine. —  For  the  ground 
color  make  a  light  wash  of  crimson  lake,  burnt  umbei,  and 
gamboge,  equal  parts.  For  graining  use  a  darker  mixture  of 
of  crimson  lake  and  burnt  umber. 

No.  7.  Convention  for  Building-stone.  —  The  ground 
color  is  a  light  wash  of  Payne's  gray  and  the  shade  lines  are 
added  mechanically  with  the  drawing-pen  or  free-hand  with 
the  writing-pen. 

No.  8.  Convention  for  Earth. — Ground  color,  India  ink 
and  neutral  tint.  The  irregular  lines  to  be  added  with  a  writ- 
ing-pen and  India  ink. 

No.  9.  Section  Lining  for  Wrought  or  Malleable  Iron. — 
When  the  drawing  is  to  be  tinted,  the  color  used  is  Prussian 
blue. 

No.  10.  Cast  Iron. — These  section  lines  should  be  drawn 
equidistant,  not  very  far  apart  and  narrower  than  the  body 
lines  of  the  drawing.  The  tint  is  Payne's  gray. 

No.  ii.  Steel. — This  section  is  used  for  all  kinds  of  steel. 
The  lines  should  be  of  the  same  width  as  those  used  for  cast- 
iron  and  the  spaces  between  the  double  and  single  lines  should 
be  uniform.  The  color  tint  is  Prussian  blue  with  enough  crim- 
son lake  added  to  make  a  warm  purple. 

No.  12.  Brass. — This  section  is  generally  used  for  all 
kinds  of  composition  brass,  such  as  gun-metal,  yellow  metal, 


24  DRA  WING  AND  DESIGNING. 

bronze  metal,  Muntz  metal,  etc.  The  width  of  the  full  lines, 
dash  lines  and  spaces  should  all  be  uniform.  The  color  tint 
is  a  light  wash  of  gamboge. 

Nos.  13-20. — The  section  lines  and  color  tints  for  these 
numbers  are  so  plainly  given  in  the  figure  that  further  in- 
struction would  seem  to  be  superfluous. 

Sometimes  draftsmen  will  Crosshatch  all  the  sectional  parts 
with  a  uniform  space  and  ilne  like  that  used  for  cast  iron  and 
mark  the  names  of  the  different  materials  or  their  initials  in 
some  convenient  place  on  the  parts  themselves.  This  does 
not  look  as  well  nor  is  it  any  more  convenient  to  experienced 
men  than  the  other  method. 

CONVENTIONAL   LINES. 

FlG.  21. — There  are  four  kinds: 

(i)  The  Hidden  Line. — This  line  should  be  made  of  short 
dashes  of  uniform  length  and  width,  both  depending  some- 
what on  the  size  of  the  drawing.  The  width  should  always 
be  slightly  less  than  the  body  lines  of  the  drawing,  and  the 


FIG.  21. 

length  of  the  dash  should  never  exceed  -J".  The  spaces 
between  the  dashes  should  all  be  uniform,  quite  small,  never 
exceeding  -fa" .  This  line  is  always  inked  in  with  black  ink. 

(2)  The  Line  of  Motion. — This  line  is  used  to  indicate 
point  paths.  The  dashes  should  be  made  shorter  than  those  of 
the  hidden  line,  just  a  trifle  longer  than  dots.  The  spaces 
should  of  course  be  short  and  uniform. 


IN  TROD  UCTOR  Y  INSTR  UCTIONS. 


'(3)  Center  Lines. — Most  drawings  of  machines  and  parts 
of  machines  are  symmetrical  about  their  center  lines.  When 
penciling  a  drawing  these  lines  may  be  drawn  continuous  and 
as  fine  as  possible,  but  on  drawings  for  reproductions  the  black- 
inked  line  should  be  a  long  narrow  dash  and  two  short  ones 
alternately.  When  colored  inks  are  used  the  center  line  should 
be  made  a  continuous  red  line  and  as  fine  as  it  is  possible  to 
make  it. 

(4)  Dimension  Lines  and  Line  of  Section. — These  lines 
are  made  in  black  with  a  fine  long  dash  and  one  short  dash 
alternately.  In  color  they  should  be  continuous  blue  lines. 
Colored  lines  should  be  used  wherever  feasible,  because  they 
are  so  quickly  drawn  and  when  made  fine  they  give  the  drawing 
a  much  neater  appearance  than  when  the  conventional  black 
lines  are  used.  Colored  lines  should  never  be  broken. 

CONVENTIONAL   BREAKS. 

FlG.  22. — Breaks  are  used  in  drawings  sometimes  to  indi- 
cate that  the  thing  is  actually  longer  than  it  is  drawn,  some- 


FIG.  22. 


26 


DRA  WING  AND  DESIGNING. 


times  to  show  the  shape  of  the  cross-section  and  the  kind  of 
material.     Those  given  in  Fig.  22  show  the  usual  practice. 


CROSS-SECTIONS. 

FlG.  23. — When  a  cross-section  of  a  pulley,  gear-wheel  or 
other  similar  object  is  required  and  the  cutting-plane  passes 
through  one  of  the  spokes  or  arms,  then  only  the  rim  and  hub 
should  be  sectioned,  as  shown  at  xx  No.  I  and  zz  No.  2,  and 
the  arm  or  spoke  simply  outlined.  Cross-sections  of  the  arms 
may  be  made  as  shown  at  AA  No.  2.  In  working  drawings  of 
gear-wheels  only  the  number  of  teeth  included  in  one  quadrant 
need  be  drawn ;  the  balance  is  usually  shown  by  conventional 
lines,  e.g.,  the  pitch  line  the  same  as  a  center  line,  viz.,  a  long 


FIG.  23. 

dash  and  two  very  short  ones  alternately  or  a  fine  continuous 
red  line. 

The  addendum  line  (d]  and  the  root  or  bottom  line  (b)  the 
same  as  a  dimension  line,  viz.,  one  long  dash  and  one  short 
dash  alternately  or  a  fine  continuous  blue  line.  The  end  ele- 
vation of  the  gear-teeth  should  be  made  by  projecting  only 
the  points  of  the  teeth,  as  shown  at  No.  2. 

Other  conventions  will  be  referred  to  in  the  text  con- 
nected with  the  figures  in  which  they  are  illustrated. 

Constructions. — To  draw  the  curve  of  intersection  that  is 
formed  by  a  plane  cutting  an  irregular  surface  of  revolution. 


INTRODUCTORY  INSTRUCTIONS.  2J 

Figs.    24  and   25    show   examples  of   engine  connecting- 
rod  ends  where  the  curve  /  is  formed  by  the  intersection  of 


FIG.  24. 

the  flat  stub  end  with  the  surface  of  revolution  of  the  turned 
part  of  the  rod. 

1    I L 


FIG.  25. 

Divide  the  line  AB,  Figs.  24  and  25,  into  any  number 
of  equal  parts  and  through  them  describe  arcs  cutting  the 
center  line  CD.  Through  the  intersections  of  these  arcs 
with  CD  draw  horizontals  to  intersect  the  curve  or  fillet  G. 


28 


DRA  WING  AND  DESIGNING. 


Through  the  intersections  on  G  draw  perpendiculars  and 
from  the  divisions  on  AB  draw  horizontals  to  intersect  the 
perpendiculars;  these  latter  intersections  are  points  in  the 
curve  /. 

The  curve  E  can  be  found  in  a  similar  way  as  shown  by 
the  figure. 

B 


FIG.  26.  FIG.  27. 

To  draw  the  projections  of  a  V-threaded  screw  and  its  nut 
of  3"  diam.  and  f"  pitch. 

Begin  by  drawing  the  center  line  Cy  Fig.  26,  and  lay  off 
on  each  side  of  it  the  radius  of  the  screw  ij".  Draw  AB 
and  6D.  Draw  A6  the  bottom  of  the  screw,  and  on  AB  step 
off  the  pitch  =  J",  beginning  at  the  point  A. 


INTRODUCTORY  INSTRUCTIONS.  CQ 

On  line  6D  from  the  point  6  lay  off  a  distance  =  half  the 
pitch  =  f",  because  when  the  point  of  the  thread  has  com- 
pleted half  a  revolution  it  will  have  risen  perpendicularly  a 
distance  =  half  the  pitch,  viz.,  f". 

Then  from  the  point  6"  on  6D  step  off  as  many  pitches  as 
may  be  desired.  From  the  points  of  the  threads  just  found, 
draw  with  the  30°  triangle  and  T-square  the  V  of  the  threads 
intersecting  at  the  points  b .  .  b .  .  the  bottom  of  the  threads. 

At  the  point  O  on  line  A6  draw  two  semicircles  with  radii 
—  the  top  and  bottom  of  the  thread  respectively.  Divide 
these  into  any  number  of  equal  parts  and  also  the  pitch  Pinto 
the  same  number  of  equal  parts.  Through  these  divisions 
draw  hors.  and  pers.  intersecting  each  other  in  the  points  as 
shown  by  Fig.  26,  which  shows  an  elevation  partly  in  section 
and  a  section  of  a  nut  to  fit  the  screw.  Through  the  points 
of  intersection  draw  the  curves  of  the  helices  shown,  using 
No.  3  of  the  "Sibley  College  Set"  of  Irregular  Curves. 

ELEMENTARY   MACHINE   DESIGN. 

A  machine,  according  to  Prof.  John  H.  Barr,  is  "a 
combination  of  resistant  bodies  for  modifying  energy  and 
doing  work,  the  members  of  which  are  so  arranged  that,  in 
operation,  the  motion  of  any  member  involves  definite,  rela- 
tive, constrained  motion  of  the  others." 

In  order  to  obtain  the  most  desirable  results  in  designing 
such  a  structure  it  is  necessary  to  give  the  several  bodies 
composing  it  such  form  and  proportion  as  will  enable  them  to 
perform  their  functions  in  the  best  possible  way  and  at  the 
same  time  present  a  pleasing  appearance  to  the  experienced 


30  DRAWING   AND    DESIGNING. 

eye.  And,  moreover,  it  must  not  be  forgotten  that  these 
desired  results  should  be  sought  with  a  due  regard  to  economy 
of  material  and  construction. 

The  form  of  a  machine  will  probably  depend  largely  upon 
the  designer's  experience  and  his  natural  ability  or  intuition. 

The  proportion  of  the  several  parts  may  be  calculated  if 
the  opposing  forces  are  known,  but  in  many  cases  these  forces 
cannot  be  accurately  determined  and  the  designer  must  rely 
upon  the  most  approved  practice  of  the  past  had  under 
similar  conditions. 


MATERIALS   USED   IN   MACHINE   CONSTRUCTION. 

The  principal  materials  used  in  machine  construction  may 
be  divided  into  three  heads,  viz. :  Cast  Metals,  Wrought 
Metals,  and  Wood. 

CAST    METALS. 

Among  the  cast  metals  the  more  important  in  machine 
construction  are  cast  iron,  malleable  cast  iron,  cast  steel, 
brass,  copper-bronze  or  gun-metal,  phosphor-bronze,  and 
aluminum. 

Cast  Iron. — Three  kinds  of  white  cast  iron  and  three  of 
gray  are  used  in  different  ways  in  machine  construction. 
The  whitest  iron  is  very  hard  and  is  used  like  the  others  of 
its  class  for  making  wrought  iron. 

The  gray  irons  do  not  melt  as  readily  as  the  white,  but 
are  more  fluid  when  melted.  The  grayest  irons  are  the 
weakest  and  are  used  only  for  mixing  with  others  in  the 
cupola. 


INTRODUCTORY  INSTRUCTIONS.  31 

Ordinary  cast  iron  contains  from  3$  to  5$  of  carbon,  which 
in  the  white  iron  is  fully  combined  with  the  iron,  while  only 
,6#  to  1.5^  is  combined  in  the  gray  iron  and  2.9$  to  3.7^ 
shows  as  graphite  crystals. 

Iron  castings  of  machine-parts  are  made  from  patterns. 
These  patterns  are  made  of  wood,  usually  soft  pine,  in  form 
exactly  like  the  castings  desired.  The  patterns  are  used  to 
make  moulds  in  sand  in  the  foundry  and  into  these  moulds  is 
poured  the  molten  iron. 

Cast  iron  after  solidifying  in  the  moulds  contracts  while 
cooling  about  •§•"  per  foot  of  length.  To  allow  for  this  con- 
traction pattern-makers  use  a  special  rule  called  a  shrink-rule 
for  measuring  patterns;  it  is  \"  per  foot  longer  than  the 
standard  rule. 

Sharp  corners  in  patterns  do  not  cast  sharp  and  square  in 
the  metal,  but  come  out  ragged  and  blunt,  so  that  whenever 
possible  sharp  edges  should  be  rounded  and  sharp  concave 
corners  filleted  or  partially  filled  in;  the  result  is  a  stronger 
and  better-looking  casting. 

To  avoid  irregular  internal  strains  in  iron  castings  when 
cooling  it  is  necessary  that  the  section  of  the  casting  be  made 
as  uniform  as  possible,  so  that  the  metal  may  contract  uni- 
formly throughout. 

Chilled  Castings. — Melted  gray  cast  iron  if  cooled  quickly 
retains  in  chemical  combination  a  large  amount  of  carbon 
which  otherwise  would  be  separated  from  the  casting.  The 
result  is  a  white  hard  iron  called  chilled  cast  iron.  To 
secure  this  quick  cooling  the  mould  into  which  the  metal  is 
cast  is  made  of  thick  cast  iron,  which  draws  the  heat  from 
the  molten  metal  in  much  less  time  than  does  the  sand  mould. 


32  DRAWING   AND   DESIGNING. 

Malleable  Castings  are  made  by  putting  a  gray-iron  cast- 
ing in  a  suitable  box  and  covering  it  with  powdered  red 
hematite,  which  is  an  oxide  of  iron,  and  keeping  it  in  a 
furnace  at  a  bright-red  heat  for  from  two  to  thirty  hours  or 
even  longer,  depending  upon  the  size  of  the  casting;  such 
castings  are  valuable  for  small  light  parts  of  machines,  because 
they  are  tough  and  strong.  Malleable  castings  can  be  worked 
like  wrought  iron,  but  will  not  weld. 

Cast  Steel  is  made  by  melting  broken  pieces  of  blister- 
steel  in  a  closed  crucible  and  casting  into  ingots. 

Brass  is  very  much  used,  because  it  is  easy  to  work,  is 
cheap,  strong,  and  tough,  and  of  a  good  color.  The  usual 
composition  of  brass  is  2  of  copper  to  I  of  zinc,  with  some- 
times a  little  lead*  added. 

Muntz  Metal  is  a  brass  composition  of  3  parts  copper  to 

2  of  zinc.      It  can  be  rolled  or  forged  when  hot  and  is  used  in 

t 

the  shape  of  bolts  and  nuts,  sheets  for  sheathing  wooden 
vessels,  and  often  takes  the  place  of  iron  or  steel  because  of 
its  ability  to  withstand  the  corrosive  action  of  water. 

Copper. — Pure  copper  with  a  small  addition  of  phos- 
phorus makes  fairly  good  castings,  but  it  is  difficult  to  obtain 
sound  castings  from  copper  alone.  Copper  has  a  reddish- 
brown  color  and  is  very  malleable  and  ductile  when  pure.  It 
can  be  hammered,  rolled,  and  forged  when  hot  or  cold;  joints 
can  be  united  by  brazing,  but  welding  is  difficult.,  The 
annealing  of  iron  and  steel  is  effected  by  heating  and  slow 
cooling,  while  copper  can  only  be  annealed  by  heating  and 
quick  cooling. 

Bronze  or  Gun-metal. — The  best  composition  is  made  of 
9  parts  of  copper  to  I  of  tin.  For  bearings  designed  to  sus- 


'INTRODUCTORY  INSTRUCTIONS.  33 

tain  great  pressure  very  hard  bronze  is  often  used,  in  which 
the  proportion  of  tin  is  increased  to  14  parts  with  86  parts  of 
copper. 

Phosphor-bronze. — This  alloy  is  made  by  adding  from 
2%  to  4#  of  phosphorus  to  the  common  bronze.  It  is  used  for 
many  things  in  place  of  iron  and  steel,  such  as  pump-rods, 
ship-propellers,  etc. ;  it  is  also  used  quite  largely  for  locomo- 
tive axle-bearings  and  shows  excellent  wearing  qualities. 

Babbitt  Metal. — This  is  a  soft  white  metal  that  is  used 
quite  largely  for  lining  shaft-bearings.  Its  composition  is 
usually  as  follows:  copper  4  parts,  antimony  8,  tin  24,  melted 
together,  and  before  using  this  alloy  is  melted  with  an  addi- 
tion of  twice  its  weight  of  tin  and  applied  to  the  bearings 
while  molten.  So  the  real  composition  of  the  lining  is  copper 
4,  antimony  8,  and  tin  96. 

Aluminum. — This  is  a  very  light  metal,  soft,  malleable, 
and  ductile,  and  of  a  silvery-white  color  with  a  bluish  tint. 
A  process  for  producing  it  with  comparative  cheapness  was 
discovered  in  1890,  and  since  then  its  production  has  been 
rapidly  increasing.  It  is  thoroughly  non-corrosive. 

WROUGHT   METALS. 

These  consist  of  wrought  iron  and  steel  of  various  qualities. 

Wrought  Iron  or  Malleable  Iron  is  a  white  metal  not 
easily  melted  and  is  very  strong  and  tough.  It  is  made  from 
the  white  cast  irons  by  abstracting  the  most  of  the  latter's  car- 
bon in  a  puddling-furnace.  It  is  taken  from  this  furnace  in 
large  spongy  masses  called  blooms,  and  shingled  by  repeated 
squeezing  and  hammering  and  rolled  into  what  is  known  as 
puddled  bars.  The  puddled  bars  are  then  cut  into  short 


34  DRAWING   AND    DESIGNING. 

pieces  and  piled  into  faggots;  these  are  heated  again  and 
rolled  into  what  is  known  as  merchant  bars.  The  best  quali- 
ties of  wrought  iron  are  piled  together,  reheated,  and  rolled 
in  the  same  way  many  times,  giving  the  iron  its  fibrous  nature 
which  makes  it  so  tough  and  strong.  A  valuable  property 
of  wrought  iron  is*  that  it  can  be  welded  at  a  temperature  of 
from  1500°  to  1600°  Fahr. 

Case-hardening. — This  is  a  hardening  of  the  surface  of 
finished  parts  of  machines,  such  as  the  links,  guides,  etc.,  of 
steam-engines,  so  that  their  wearing  qualities  are  very  much 
increased.  It  is  effected  as  follows:  the  piece  to  be  case- 
hardened  is  placed  in  a  suitable  receptacle  and  surrounded  by 
bone-dust,  horn-shavings,  yellow  prussiate  of  potash,  or  any 
such  substance  that  is  rich  in  carbon,  and  heated  to  about  a 
red  heat,  when  the  wrought  iron  will  absorb  some  of  the 
carbon  surrounding  it  and  be  converted  into  steel,  which  can 
be  hardened  by  immersing  in  water. 

Steel  is  made  from  wrought  iron  by  adding  a  little  carbon 
or  from  cast  iron  by  extracting  some  of  its  carbon.  There 
are  three  ways  of  doing  this:  the  Bessemer,  Siemens-Martin, 
and  cementation  processes. 

Bessemer  Steel  is  made  by  pouring  melted  cast  iron  into  a 
converter  through  which  a  blast  of  air  is  forced.  In  this 
way  the  carbon  in  the  cast  iron  is  burnt  out,  leaving  almost 
pure  iron.  To  this  is  added  a  certain  quantity  of  spiegeleisen, 
which  is  a  compound  of  iron,  carbon,  and  manganese,  and 
then  the  molten  metal  is  cast  into  steel  ingots. 

Siemens-Martin  Steel  is  made  by  melting  wrought  iron 
and  cast  iron,  or  cast  iron  and  certain  kinds  of  iron  ore, 
together  on  the  hearth  of  a  reverberatory  gas-furnace. 


INTRODUCTORY  INSTRUCTIONS.  35 

The  Cementation  Process  consists  of  embedding  bars  of 
wrought  iron  in  powdered  charcoal  in  a  fire-clay  trough  and 
placed  in  a  furnace  for  several  days  at  a  high  temperature. 
The  iron  combines  with  portions  of  the  carbon  and  forms 
blister-steel,  so  called  from  the  blisters  found  on  its  surface. 
Bars  of  blister-steel  about  18"  long  are  then  bound  together 
by  strong  steel  wire  and  heated  to  a  welding  heat,  then 
hammered  and  rolled  into  bars  called  shear-steel. 

WOODS. 

The  woods  used  in  machine  construction  are  principally 
pine,  fir,  beech,  boxwood,  ash,  elm,  hornbeam,  lignum-vitae, 
mahogany,  oak,  and  teak. 

Pine  and  Fir  are  strong,  cheap,  and  easy  to  work,  and  are 
largely  used  for  a  variety  of  purposes. 

White  and  Yellow  Pine  are  much  used  in  pattern-making. 

Beech  is  used  for  the  cogs  of  mortise-wheels;  it  takes  a 
smooth  surface  and  is  very  close-grained. 

Boxwood  is  much  used  for  sheaves  of  pulley-blocks  and 
bearings.  It  takes  a  smooth  surface,  is  hard,  heavy,  and  of 
a  bright-yellow  color. 

Elm  is  very  durable  in  water,  and  is  therefore  used  for 
paddle-wheel  floats,  piles,  etc. 

Hornbeam  is  often  used  for  cogs  of  mortise-wheels. 

Lignum-vitae.  —  This  is  a  very  hard  wood  of  great 
strength  and  durability  under  water.  For  these  reasons  it  is 
used  for  bearings  under  water  and  other  purposes  requiring 
hardness  and  strength.  Its  specific  gravity  is  1.33;  i.e.,  \\ 
times  the  weight  of  the  same  volume  of  water. 

Mahogany  is  a  favorite  for  making  small  patterns.      It  is 


36  DRAWING   AND    DESIGNING. 

straight-grained,  strong,  and  durable,  and  does  not  as  readily 
change  its  form  when  seasoning  as  most  other  woods. 

Oak  is  tough  and  straight-grained,  very  durable,  whether 
used  dry  or  in  water.  It  is  used  for  machine-framing  and 
supports. 

Teak  is  a  strong,  tough,  durable  wood.  It  shrinks  very 
little  when  seasoning,  and  is  very  valuable  on  that  account. 
Bolts  passing  through  it  are  prevented  from  rusting  by  the  oil 
it  contains. 


STRENGTH   OF   MATERIALS. 
DEFINITIONS. 

Load. — The  load  on  any  member  of  a  machine  is  a  total 
of  the  external  forces  acting  on  it.  The  useful  load  is  the 
load  which  the  member  is  designed  to  carry  outside  of  itself; 
e.g.,  the  useful  load  on  the  springs  of  a  railway-car  is  the  load 
which  may  be  placed  upon  the  car  in  addition  to  the  load 
arising  from  the  weight  of  the  car  itself.  A  live  load  is  a 
variable  load  applied  and  removed  continuously.  A  dead 
load  or  constant  load  is  that  which  has  an  unvarying  and 
continuous  straining  action. 

Strain  and  Stress. — Strain  is  the  change  of  form  pro- 
duced by  the  action  of  a  load.  If  the  load  does  not  exceed 
the  elastic  limit  of  the  material  the  strain  will  disappear  when 
the  load  is  removed.  Machine-members  should  be  designed 
strong  enough  to  resist  permanent  set  under  maximum  load. 

Stress  is  the  force  which  causes  strain.  The  different 
kinds  of  stress  are:  tensile  stress  or  pull,  compressive  stress  or 


IN  TROD  UCTOR  Y  INS  TR  UCTIONS. 


37 


thrust,  shearing  stress  or  cross-cutting,  bending  or  combined 
thrust  and  pull,  and  torsional  or  twisting  stress. 

Resistance  of  metal  to  change  of  form  is  due  to  the 
inherent  cohesive  force  of  its  molecules. 

Elasticity  or  spring  is  the  inherent  property  in  a  material 
of  regaining  original  form  after  an  external  load  has  been 
removed. 

Elastic  Limit. — The  elastic  limit  is  the  limit  of  extension 
or  compression  to  which  a  material  can  be  subjected  without 
permanent  set.  Within  the  elastic  limit  strain  and  stress  are 
proportional. 

Modulus  of  Elasticity. — Dr.  Thomas  Young  of  the 
British  Royal  Society  propounded  the  following  formula  for 
the  modulus  of  elasticity  (E)  in  1826,  known  as  "  Young's 
Modulus  " : 

stress  per  sq.  in.  in  Ibs. 

E  = —        .     . — j-: -r  (within  the  elastic  limit). 

strain  per  inch  of  length  v 

TABLE    1. 
ELASTIC  MODULI. 


Material. 

Modulus  of 
Elasticity. 

Material. 

Modulus  of 
Elasticity. 

\Vrought  iron   bars.  .  .  • 

2Q  OOO  OOO 

Pine    average  

S 
500  ooo 

Wrought  iron    plates 

26  ooo  ooo 

Beech   

350  ooo 

Cast  steel  

30  ooo  ooo    ! 

800  ooo 

Cast  steel,  tempered.  .  . 
Fortjed  steel     

36,000,000   1 
30  ooo  ooo    ' 

Ash  

Elm 

,600,000 

Steel  plates  

31  ooo  ooo 

Lignum-vitae   •  • 

Cast  iron    average.  .  •  . 

17  OOO  OOO     i 

Mahogany  ....        .    .  . 

300  ooo 

Brass  and  bronze  

12  OOO  OOO     | 

Oak    English  

700  ooc 

14  ooo  ooo 

Teak    

2  300  OOO 

12'  OOO  OOO 

Lead    sheet     •  •      • 

72O  OOO     1 

Glass    plate 

*0»3W 

1 

Ultimate  Strength  is  the  smallest  load  that  will  fracture 
a  member  under  stress. 


DRA  WING   AND   DESIGNING. 


The  Proof  Strength  is  nearly  equal  to  the  load  that  will 
cause  permanent  set;  i.e.,  to  the  maximum  elastic  resistance. 

The  Factor  of  Safety  is  the  ratio  of  the  ultimate  strength 
of  a  member  to  the  working  load,  or  the  breaking  load  to  the 
actual  load.  The  factor  of  safety  changes  for  different 
materials  and  for  different  uses  of  the  same  material.  It  is 
of  course  much  greater  under  live  loads  than  under  constant 
dead  loads. 

The  following  table  gives  the  ordinary  factors  of  safety  in 
general  use: 

TABLE  2. 

FACTORS  OF  SAFETY. 


Material. 

Ratio  of  Ultimate  Load  to  Working  Load. 

Dead  Load. 

Live  Load. 

Shocks. 

4 

3 
3 
3 

5 
8 

10 

7 
5  to  8 
5  to  8 
5  to  8 
8 

10 

20 

15 
9  to  13 
9  to  13 
10  to  15 
10  to  15 
14  to  18 
30 

Mild  steel    

Cast  steel             

Copper  and  similar  metals  and  alloys 
Wood  

Strength  of  Cast  Iron. — The  average  American  cast  iron 
has  a  tenacity  of  about  20,000  Ibs.  per  sq.  in.,  but  cast  iron 
has  been  made  which  showed  an  ultimate  tensile  strength  of 
35,000  Ibs.  per  sq.  in. 

The  ultimate  compressive  strength  of  cast  iron  is  from  4  to 
6  times  its  tenacity, — the  average  is  about  90,000  Ibs.  per  sq. 
in., — and  the  average  shearing  strength  is  about  20,000  Ibs. 
per  sq.  in.  The  elastic  limit  of  cast  iron  is  from  £  to  nearly 
equal  to  the  breaking  strength. 


INTRODUCTORY  INSTRUCTIONS.  39 

Strength  of  Wrought  Iron. — The  elastic  strength  of 
wrought  iron  is  usually  over  half  its  ultimate  strength;  good 
bars  and  plates  will  show  an  elastic  limit  of  about  26,000  Ibs. 
In  ascertaining  the  strength  of  a  particular  piece  of  wrought 
iron  it  will  be  necessary  to  know  the  elongation  per  cent  of 
specimen.  The  elongation  is  greater  for  short  than  for  long 
specimens.  The  usual  length  of  specimens  for  tensile  test 
is  8".  Wrought  iron  loses  its  strength  in  forging;  this  loss 
of  strength  is  equal  to  about  20$.  The  difference  between 
the  strength  of  wrought  iron  when  pulled  against  the  grain 
and  in  the  direction  of  the  grain  is  from  3000  to  9000  Ibs.  per 
sq.  in.,  the  strength  in  the  direction  of  the  grain  being  the 
greater.  The  tensile  strength  of  wrought  iron  varies  from 
40,000  to  60,000  Ibs.  per  sq.  in. 

Strength  of  Steel.— The  steel  cast  from  blister-steel  is 
the  strongest,  having  a  tensile  strength  of  from  100,000  to 
130,000  Ibs.  per  sq.  in.,  but  it  is  hard  and  brittle,  with  an 
elongation  of  only  about  5$.  It  is  therefore  unsuitable  for 
constructive  purposes.  A  good  plate  steel  for  steam-boilers 
has  a  tensile  strength  of  from  55,000  to  60,000  Ibs.,  with  an 
elongation  of  about  20^  in  a  length  of  8". 

The  following  tables  were  compiled  after  consulting 
various  authorities;  e.g.,  Thurston,  Unwin,  Kent,  Moles- 
worth,  etc. 


4o 


DRA  WING   AND    DESIGNING. 


TABLE   3. 

AVERAGE  ULTIMATE  AND  ELASTIC  STRENGTH  OF  VARIOUS  MATERIALS  AND 
MODULI  OF  ELASTICITY  IN  POUNDS  PER  SQUARE  INCH. 


Ultimate  Strength. 

Elastic  Strength. 

c 

C 

E. 

E'. 

Material. 

.2 

With  the 

Trans- 

1 

c 

I 

a 

a 

bo 
c 

| 

c 

.2 

%    ' 

% 

I 

t 

1 

Grain. 

verse. 

£ 

0 

u 

3i 

C/} 

'I 

d 

I 

Cast  iron,  common. 

20,000 

90,000 

20,000 

12,000 

23,000 

9,000 

15,000,000 

7,000,000 

Wrought  iron,  bars.. 

50,000 

48,000 

40,000 

26,OOO 

26,000 

22,000 

29,000,000 

10,500,000 

Wrought  iron,  plates. 
Wrought  shape  iron.. 

48,000 
48,000 

46,000 
46,000 

38,000 
38,000 

26,000 
26,OOO 

26,000 
26,000 

22,000 
22,OOO 

29,000,000 
29,000,000 

10,000,000 

10,000,000 

Wrought     stay  •  bolt 

iron    

5I,OOO 

49,000 

40,000 

28.OOO 

28,000 

24,OOO 

29,000,000 

10,000,000 

Wrought  rivets  ..... 

50,000 

48,000 

38,000 

26,OOO 

26,000 

22,000 

29,000,000 

10,000,000 

Malleable  cast  iron... 

32,OOO 



38,000 

23.500 

27,000 

2O.OOO 

24,500,000 

13.500,000 

Cast  steel  ........... 

88,000 

125,000 

64.000 

7O,OOO 

64,000 

30,000,000 

11,000,000 

Soft-steel  plates  

55,000 

66,000 

50,000 

32,000 



25,000 

30,000,000 

11,000,000 

Steel  rivets...  .  .    . 

52,665 

50,000 

45,000 

29,OCO 

29,000,000 

10,500,000 

Cast  copper.  

23,OOO 

45,000 

5,9OO 

£ 

Wood  pine 

6  ooci 

650 

Wood  oak  English 

Leather  .   . 

6,000 

Wrought  Iron  has  a  specific  gravity  of  7.5  to  7.8  accord- 
ing to  its  chemical  composition  and  physical  structure. 

Cast  Iron  has  a  specific  gravity  of  7.25. 

The  tensile  strength  of  metals  varies  with  their  tempera- 
ture, generally  decreasing  as  their  temperature  is  increased. 


Lead  .  .  .  . 
Tin  .  .  .  . 
Zinc  .  .  .  . 
Worked  copper 


TABLE   4. 

RELATIVE  TENACITIES  OF  METAL.     (THURSTON.) 

Cast  iron  . 


.   i.o 
•   1.3 

.    2.O 
12  tO  20 


7  tO  12 


Wrought  iron     .     .  20  to  40 
Steel 40  to  loo 


USEFUL    TABLES    AND    MISCELLANEOUS 
INFORMATION. 


WEIGHTS    AND    MEASURES. 

AVOIRDUPOIS^COMMERCIAL                          SQUAR£  MEASURE. 

16  drachms      ....      ounce.          144  square  inches      .       square  foot. 

16  ounces pound.            9                 feet  .     .                    yard. 

14  pounds stone.             30^              yards  .     .                    rod. 

28        "         quarter.        40       "        rods  .     .           '        rood. 

4  quarters      ....      cwt.                  4                roods  .     .                    acre. 

2240  pounds ton.           ;  640                acres  .     .           '         mile. 

MEASURE  OF  VOLUME. 

A  cubic  foot  has 1728  cubic  inches. 

An  ale  gallon  has 282 

A  standard  or  wine  gallon  has 231 

A  dry  gallon  has 268.8  " 

A  bushel  has 2150.4  " 

A  cord  of  wood  has 128              feet. 

A  perch  of  stone  has 24.75" 

A  ton*of  round  timber  has 40      ." 

A       "      hewn         "        "         50 

A  box  19!     X  19!  inches,  19!  inches  deep,  contains  .     .  I  barrel. 

A     "     I2^|  X  i2^|     "        i2Tf     "                                    .     .  i  bushel. 

A    "       8£    X     8£  .    "         8$       "                                    .     .  i  peck. 

A     "       6T7$  X    6T'5     "         6T*g                                          .     .  4 

A     '        4TV  X    4TV                4iV                                            .     .  I  quart. 

An  acre  contains 4840  square  yards. 

209  feet  long  by  209  feet  broad  is i  acre. 

TABLE  OF  DISTANCE. 


A  mile  is    ... 
A  knot  is    ... 
A  league  is 
A  fathom  is    . 
A  metre  is  nearly 
A  hand  is  ... 
A  palm  is  ... 
A  span  is    ... 


5280  feet  or  1760  yards. 
6086  feet. 

3  miles. 
6  feet. 

3  feet  3!  inches. 

4  inches. 
3       " 

9 


MEASURE  OF  LENGTH. 


12  incnes 
3  feet  . 
2  yards 

i6i  feet. 


i  foot, 
i  yard, 
i  fathom, 
i  rod. 


4  rods  .     . 

10  chains    . 

8  furlongs 

3  miles      . 


T  chain, 
i  furlong, 
i  mile, 
i  league. 

41 


DRAWING   AND    DESIGNING. 


Each  nominal  horse-power  of  boilers  requires  I  cubic  foot  of  water  per 
hour. 

In  calculating  horse-power  of  steam-boilers  consider  for — 
Tubular  boilers  15  sq.  ft.  of  heating-surface  equivalent  to  I  horse-power. 
Flue  boilers  12  sq.  ft.  of  heating-surface  equivalent  to  I  horse-power. 
Cylinder  boilers  10  sq.  ft.  of  heating-surface  equivalent  to  I  horse-power. 

To  find  the  area  of  a  piston,  square  the  diameter  and  multiply  by  .7854. 

To  find  the  pressure  in  pounds  per  square  inch  of  a  column  of  water, 
multiply  the  height  of  the  column  in  feet  by  .434. 

A  horse-power  in  machinery  is  estimated  at  33,000  pounds  raised  one 
foot  high  in  a  minute,  or  one  pound  raised  33,000  feet  high  in  a  minute. 

Iron  under  the  influence  of  the  hammer  and  of  constant  use  gradually 
assumes,  by  repeated  vibration,  a  different  texture  from  that  it  had  when 
the  piece  was  new.  The  metal  becomes  crystalline,  loses  its  tenacity, 
and  becomes  brittle. 

WEIGHT    OF   WATER. 

One  cubic  foot  at  39.1°  F.  =  62.425  Ibs.,  at  212°  F.  =  59.833.  At  62°  F. 
the  weight  varies  from  62.291  to  62.360.  The  figure  generally  believed  to 
be  the  most  accurate  is  62.355.  Weight  of  I  gallon  at  39.2°  —  8.3389  Ibs. 

WEIGHTS    OF   CAST-IRON    WATER-PIPES. 
IN  POUNDS  PER  FOOT  RUN,  INCLUDING  BELLS  AND  SPIGOTS. 


Diameter. 

Philadelphia 
Water-works. 

Chicago 
Water-works. 

Cincinnati. 

Regular 
Standard. 

Light. 

Weight. 

Thickness. 

7 
15 

22 

33 
42 
60 

75 

6 
13 

20 

30 
40 

55 
70 

3           
4           ... 
6 
8          

10             ...  . 
12              .... 

16          

20             .... 

2/1 

15.000 
21.  Ill 
30.  106 
40.683 
52.075 
69.162 
102.522 
147.681 

17 
23 
50 
65 
80 
100 
130 
200 
224 
300 
430 

i' 

r 

r 
i" 

4" 

24.167 
36.666 
50  .  ooo 
65.000 

83.333 

125.000 

250.000 

an 

76 

450.000 

yj          .... 

Water-pipe  is  usually  tested  to  300  pounds  pressure  per  square  inch 
before  delivery,  and  a  hammer  test  should  be  made  while  the  pipe  is  under 
pressure. 

The  Cincinnati  lengths  are  uniform  for  all  diameters,  12  feet  exclusive 
of  bell. 

Standard  lengths  ate  for  2-inch  pipe  8  feet,  and  all  other  sizes  12  feet. 


USEFUL    TABLES  AND    MISCELLANEOUS  INFORMATION.   43 

THICKNESS    OF   CAST-IRON    WATER-PIPE. 

The  following  formula,  adapted  from  Neville,  is  believed  to  be  a  safe 
equation  for  the  thickness  of  cast-iron  pipe  for  public  water-supply: 


where  /  =  thickness  of  pipe  in  inches, 

h  =  head  or  pressure  in  feet, 

d  =  diameter  of  pipe  in  inches, 

S  =  the  tensile  strength  of  metal  in  tons  of  2000  pounas. 
What  should   be  the   thickness  of   a  2O-inch   water-main  subject  to  a 
maximum  pressure  of  150  pounds  per  square  inch,  or  150  X  2.308  =  346.2 
feet  head,  with  cast-iron  of  18,000  pounds  tensile  strength  ? 


j  X  2oJ 


.32  =  .9757"- 


What  should  be  the  thickness  of  4O-inch  pipe  for  same  service  and  of 
same  metal  ? 

9        F  /346-2  \  "1 

/  =  -  X  I    .ooi6(  —  +  loj  X  40     +  .32  =  1.6313" 

The  speed  at  which  millstones  should  be  run  is 

For  3-feet  stones      .......  230  to  250  revolutions  per  minute. 

"    3i  "         "  -     •     •     •     •'  *    ...    •   ^.     200 

"    4    "         "  .....  •'•-..     .     .     180 

44     4i  "         "  .....     i-   .     .     .     160 

Speed  of  bolting-reels       .     .     .     .     .     .30  to  35 

"        "  conveyers  for  flour     ....  35  to  40  *' 

"    wheat       .     .     .  45  to  50 
"        "  elevators  ........  30  to  35 

"  smut-machines  from  550  to  700  revolutions  per  minute,  accord- 

ing to  size  of  machine. 

For  merchant  mills  allow  20  horse-power  to  a  pair  of  burrs  (4  feet),  and 
the  necessary  machinery  for  cleaning  and  bolting;  and  for  country  mills 
about  10  horse-power  to  a  pair  of  burrs. 

For  a  single  upright  saw  allow  10  horse-power,  speed  about  150  revolu- 
tions per  minute. 

For  circular  saws  the  best  average  working  speed  is 


650  to  700  rev.  per  min.  for  36-in.  saw. 
60010650    "      "      "      "   40  "     " 
55010600    "      42  "     " 


50010  525  lev.  permin.for48-in.saw. 
47510500    "      "      "      "   54  "     " 

40010450 60  "     " 

52510550    "      "      "      "44 

A  6o-saw  gin  requires  6  horse-power  to  gin  500  pounds  of  lint  in  2  hours. 

A  sumac-mill  requires  15  horse-power. 


44 


DRAWING   AND    DESIGNING. 


To  reduce  for  round  cores  and  core-prints,  multiply  the  square  of  the 
diameter  by  the  length  of  the  core  in  inches,  and  the  product  by  0.017  -s 
the  weight  of  the  pine  core,  to  be  deducted  for  the  weight  of  the  pattern. 


SHRINKAGE    OF    CASTINGS. 


Pattern-maker's  rule 
should  be  for 


of  an  inch  longer  per 
linear  foot. 


PROPERTIES    OF    THE   CIRCLE. 

Diameter    X  3.14159  =  circumference. 
Diameter    X     .8862    =  side  of  an  equal  square. 
Diameter    X     .7071     =  side  of  an  inscribed  square. 
Diameter2  X     .7854    =  area  of  circle. 
Radius         X  6.28318  =  circumference. 
Circumference  -5-  3.14159  =  diameter. 


WROUGHT-IRON   WELDED    TUBES    FOR   STEAM,    GAS,    OR 

WATER. 


Nominal 
Diameter. 

Actual  Inside 
Diameter. 

Actual  Outside 
Diameter. 

Thickness. 

Weight  per 
Footof  Length. 

No.  of  Threads 
per  Inch  of 
Screw. 

Inches. 

Inches. 

Inches 

Inches. 

Pounds. 

\ 

.270 

.405 

.068 

.243 

27 

I 

.364 

•54 

.088 

.422 

18 

I 

.494 

.675 

.091 

.561 

18 

i 

.623 

.84 

.109 

.845 

14 

i 

.824 

1.05 

•113 

1  .126 

14 

i 

1.048 

I.3I5 

•134 

1.670 

1I| 

a 

1.380 

1.66 

.  140 

2.258 

Hi 

i| 

1.611 

1.9 

.145 

2.694 

Ml 

2 

2.067 

2-375 

•154 

3.667 

II* 

2* 

2.468 

2.875 

.204 

5-773 

8 

3 

3-067 

3-5 

.217 

7-547 

8 

3* 

3.548 

4.0 

.226 

9-055 

8 

4 

4.026 

4-5 

.237 

10,  728 

8 

4i 

4-508 

5-0 

.247 

12.492 

8 

5 

5.045 

5-563 

•259 

14.564 

8 

6 

6.065 

6.625 

.280 

18,767 

8 

7 

7.023 

7.625 

.301 

23-410 

8 

8 

7.982 

8.625 

.322 

28.348 

8 

9 

9.001 

9.688 

•344 

34.077 

8 

10 

10.019 

10.75 

•366      , 

40  .  64  i 

8 

USEFUL    TABLES  AND    MISCELLANEOUS  INFORMATION.   45 


DIFFERENT   COLORS 
Cent.  Fahr. 


210 
221 
256 
26l 
370 

500 


525 

700 

800 

900 

IOOO 

IIOO 

1200 

1300 

I4OO 

1500 

I600 


4IO 
430 

493 
502 
680 

932 


977 
1292 
1472 

1657 

1832 

2OI2 
2192 
23*72 
2552 
2733 
2912 


OF    IRON    CAUSED    BY    HEAT.    (POUILLET.) 

Color. 

Pale  yellow. 
.  Dull  yellow. 
.  Crimson. 

.  Violet,  purple,  and  dull  blue;  between  261°  C. 
and  370°  C.  it  passes  to  bright  blue,  to  sea- 
green,  and  then  disappears. 

.  Commences  to  be  covered  with  a  light  coat- 
ing of  oxide;  loses  a  good  deal  of  its 
hardness,  becomes  much  more  impressible 
to  the  hammer,  and  can  be  twisted  with 
ease. 

.     Becomes  nascent  red. 

.     Sombre  red. 

.     Nascent  cherry. 

.     Cherry. 

.     Bright  cherry. 

.     Dull  orange. 
Bright  orange. 

.     White. 

.     Brilliant  white — welding  heat. 

.     Dazzling  white. 


TABLE   OF   DECIMAL   EQUIVALENTS    OF   ONE    INCH. 


1/64 

.015625 

17/64 

.265625 

33/64 

.51562-5 

49/64 

.765625 

1/32 

.03125 

9/32 

.28125 

17/32 

.53125 

25/32 

.78125 

3/64 

.046875 

19/64 

.296875 

35/64 

.546875  ' 

51/64 

•796875 

1/16 

.0625 

5/i6 

.3125 

9/16 

•  5625 

13/16 

.8125 

5/64 

.078125 

21/64 

.328125 

37/64 

.578125  • 

53/64 

.828125 

3/32 

•09375 

11/32 

-34375 

19/32. 

•  59375 

27/32 

.84375 

7/64 

•109375 

23/64 

-359375 

39/64 

•609375 

55/64 

.859375 

1/8 

.125 

3/8 

•375 

5/8 

.625 

7/8 

•875 

9/64 

.  140625 

25/64 

.390625 

41/64 

.640625 

57/64 

.890625 

5/32 

.15625 

13/32 

.40625 

21/32 

.65625 

29/32 

.90625 

11/64 

•171875 

27/64 

.421875 

43/64 

.671875 

59/64 

.921875 

3/i6 

.1875 

7/16 

•4375 

11/16 

.6875 

15/16 

.9375 

13/64 

.203125 

29/64 

.453125 

45/64 

.703125 

61/64 

.953125 

7/32 

.21875 

15/32 

.46875 

23/32 

.71875 

31/32 

.96875 

15/64 

•234375 

3i/64 

.484375 

47/64 

•734375 

63/64 

•984375 

i/4 

•  25 

1/2 

.50 

3/4 

•  75 

1 

i 

46 


DRAWING   AND    DESIGNING. 


MELTING-POINT    OF    METALS,   ETC. 


Names.  Fahr. 

Platina 459O° 

Antimony 842 

Bismuth 487 

Tin 475 

Lead 620 

Zinc 700 

Cast  iron                                        .  2100 


Names.  Fahr. 

Wrought  iron 2900° 

Steel 2500 

Copper 2000 

Glass 2377 

Beeswax 151 

Sulphur 239 

Tallow 92 


TABLE   5. 
WEIGHT  OF  VARIOUS  SUBSTANCES. 

RULE. — Divide   the   specific    gravity  of   the    substance    by  16  and    the 
quotient  will  give  the  weight  of  a  cubic  foot  of  it  in  pounds. 


Substances—  Metals. 

Specific 
Gravity. 

«!' 

<O>-i 

4-1     '-> 

11 

«u 

£ 

Substances  —  Metals. 

>, 

ll 
M 

c/} 

Weight  of  a 
Cubic  Inch. 

Aluminum  •  

2  560 

0926 

II   352 

4106 

Brass    plate.  •  

8  380 

W*  T 

Lead    rolled  

II  388 

4.1  IQ 

Brass    wire    

8  214 

2Q72 

Mercury,    -f-  32°  ....... 

13  5Q8 

4Ql8 

8  700 

•2T47 

Mercury          60°  

13   ^80 

4OI2 

8  788 

1  17Q 

Mercury        212°   

13  37O 

4.836 

8  698 

-3  T/l6 

Steel    plates  

7  806 

2823 

8  880 

TO  12 

Steel    soft  

7  833 

.  2833 

7  2O7 

.  2607 

Steel    wire.  •  » 

7  84.7 

2838 

Iron,  cast,  gun-metal   . 

7,308 
7  788 

.264 

28l7 

Tin,  Cornish,  hammered 

7,390 
6  861 

.2673 
.2482 

77O4 

2787 

7   IQI 

26 

TABLE   6. 
WEIGHT  OF  TIMBER  PER  CUBIC  FOOT. 


Ash 46  Ibs. 

Beech 44  " 

Birch 45  " 

Boxwood 62  " 

Elm 34  " 

Larch 34  " 

Lignum-vitae 80  " 


Mahogany,  Honduras    .     .     35   Ibs. 
Spanish  ...     53     " 

Oak,  English 54     " 

Pine,  red 30  to  44  " 

"      yellow      .     .     .     .    29  to  41  " 
"      white 30     " 

Teak 41  to  55  " 


USEFUL    TABLES  AND    MISCELLANEOUS  INFORMATION.    4/ 


CIRCUMFERENCES    AND    AREAS    OF   CIRCLES    ADVANCING    BY 

EIGHTHS. 


Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

Diam. 

Circum. 

Area. 

1/64 
1/32 

.04909 
.09818 

.00019 
.00077 

2  11/16 
3/4 

8.4430 
8.6394 

5-6727 
5-9396 

6  5/8 
3/4 

20.813 
21.206 

34-472 

3/64 

.14726 

.00173 

13/16 

8-8357 

6.2126 

7/8 

21.598 

37.122 

1/16 

.19635 

.00307 

7/8 

9.0321 

6.4918 

3/32 

.29452 

.00690 

15/16 

9.2284 

6-7771 

7 

21.991 

38-485 

1/8 

•39270 

.01227 

1/8 

22.384 

39-871 

5/32 

.49087 

.01917 

3 

9.4248 

7.0686 

.1/4 

22.776 

41.282 

•58905 

.02761  , 

1/16 

9.6211 

7-3662 

3/8 

23.169 

42.718 

7/32 

.68722 

.03758  ' 

1/8 

9.8175 

7.6699 

1/2 

23.562 

44-179 

•78540 

.04909 

3/T6 

10.014 

7-9798 

5/8 

23-955 

45-664 

9/32 

•88357 
•98175 

.06213 
.07670 

5/i6 

10.210 
10.407 

8.2958 
8.6179 

3/4 

7/8 

24-347 
24.740 

47-173 
48.707 

»/32 

1.0799 

.09281 

3/?6 

10.603 

8.9462 

3/8 

1.1781 

.11045 

10  799 

9.2806 

8 

25.  133 

50.265 

13/32 

1.2763 

.12962 

1/2 

10.996 

9.6211 

j/8 

25.525 

51.849 

7/16 

1-3744 

•1503^ 

9/16 

11.192 

9.9678 

i/4 

25.918 

53-456 

15/32 

1.4726 

•'7257 

5/8 

11.388 

10.321 

3/8 

26.311 

55-o88 

1/2 
17/32 

1.5708 
1.6690 

•'9635 
.22166 

11/16 

3/4 

"•585 
11.781 

10.680 
11-045 

1/2 
5/8 

26.704 
27.096 

56-745 
58.426 

9/16 

1.7671 

.24850 

13/16 

11.977 

11.416 

27.489 

60.132 

'9/32 

1.8653 

.27688 

7/8 

12.174 

1  1  -  793 

7/8 

27.882 

61.862 

5/8 

1-9635 

.30680 

15/16 

12.370 

12.177 

21/32 

2.0617 

•33824 

9 

28.274 

63.617 

11/16 

2.1598 

.37122 

4 

12.566 

12.566 

1/8 

28.667 

65-397 

73/32 

2.2580 

•43574 

1/16 

12.763 

12.962 

29.060 

67.201 

3/4 

2.3562 

•44179 

I/86 

12-959 

13.364 

3/8 

29.452 

69.029 

25/32 

2-4544 

.      -47937 

13-155 

13-772 

i/a 

29.845 

70  .  882 

13/16 

2.5525 

•51849 

i/4 

13-352 

14.186 

5/8 

30-238 

72.760 

27/32 

2.6507 

•55914 

5/t6 

13-548 

14.607 

3/4 

30-631 

74.662 

7/8 

2.7489 
2.8471 

.60132 
•64504 

13-744 
13.941 

7/8 

31-023 

76.589 

15/16 

2.9452 

.69029 

1/2 

14-I37 

i5.Q<>4 

10 

31.416 

78.540 

31/32 

3-0434 

.73708    ; 

9/16 
5/8 

14-334 
14-53° 

16-349 
16.800 

V8 

31-809 
32.201 

80.516 
82.516 

I 

3-i4i6 

.7854 

11/16 

14  726 

17-257 

3/8 

32-594 

84-541 

1/16 

3-3379 

.8866 

3/4 

14-923 

17.728 

1/2 

32.987 

86.590 

1/8 
3/t6 

3-5343 
3-7306 

.9940 
.1075 

13/16 
7/8 

15-119 
I5-3I5 

18.190 
18.665 

5/8 
3/4 

33-379 
33-772 

88.664 
90.763 

1/4 

3.9270 

.2272 

15/16 

15-512 

19.147 

7/8 

92.886 

5/i6 

4-1233 

.353°    ; 

3/8 

4-3197 

.4849 

5 

15.708 

19.635 

II 

34-558 

95-033 

7/i6 

4-5160 

.6230 

1/16 

15.904 

20.129 

1/8 

34-950 

97.205 

1/2 

9/16 

4.7124 
4.9087 

.7671 
.9175 

3/16 

16.101 
16.297 

20.629 
21.135 

3/8 

35-343 
35-736 

99.402 
101.62 

5/8 

5-1051 

•0739 

i/4 

i6.493 

21.648 

1/2 

36.128 

103.87 

11/16 

5-3014 

.2365 

5/i6 

16.690 

22.166 

5/8 

36.521 

106.  14 

3/4 

5.4978 

•4053 

3/8 

16.886 

22.691 

3/4 

36-914 

108.43 

13/16 

5.6941 

.5802 

7/16 

17.082 

23.221 

7/8 

37.306 

110.75 

7/8 

.7612 

1/2 

17-279 

23-758 

15/16 

•6.0868 

•9483  : 

9/16 

5/8 

17-475 
17.671 

24.301 
24.850 

13 

1/8 

37.699 
38.092 

113.10 
115-47 

3 

6.2832 

.,416 

11/16 

17.868 

25.406 

38.485 

117.86 

3/8 
^ 

7.4613 
7.6576 

•4301 
.6664 

6    1/8 

19.242 

29-465 

3/8 

1/2 

38.877 
39.270 

120.28 
122.72 

7-8540 

.9087 

i/4 

19-635 

30.680 

5/8 

39.663 

125-19 

9/16 
5/8 

8.0503 
8.2467 

5.1578 
5-4119 

3/8 

1/2 

20.028 
20  .  420 

3i.9i9 
33-183 

$ 

40.055 
40.448 

127.68 
130-19 

To  find  the  weight  of  castings  by  the  -weight  of  pine  patterns,  multiply  the 
weight  of  the  pattern  by  12  for  cast  iron,  13  for  brass,  19  for  lead,  12.2  for 
tin,  14.4  for  zinc,  and  the  product  is  the  weight  of  the  casting. 


47' 


DRAWING    A&D    DESIGNING. 


Number. 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

.1 
•15 

.2 

•25 

•3 
•35 

.01 

.0225 
.04 
.0625 
.09 
.1225 

.001 

.0034 
.008 
.0156 
.027 
.0429 

.3162 

.3873 
.4472 
.500 

•5477 
.5916 

.4642 

.5313 
.5848 
.6300 
.6694 
.7047 

•4 
•45 

•5 

i5  • 
.65 

.16 

.2025 
•25 
.3o25 
•36 
.4225 

.064 
.0911 
.125 
.1664 
.216 
.2746 

•6325 
.6708 
.7071 
.7416 
.7746 
.8062 

•72f 
.7663 

•7937 
.8193 

•8434 
.8662 

.7 

•75 
.8 

•«5 
•9 
•95 

.7225 
.81 
.9025 

•343 
.4219 
.512 
.6141 
.729 
.8574 

.8367 
.8660 
.8944 
.9219 
.9487 
•9747 

.8879 
.9086 
.9283 
•9473 
•9655 
.9830 

i 

2 

3 

4 
5 

i 
4 

J 

25 

i 
8 

27 
64 
125 

I.OOOO 

1.4142 
1.7321 

2.0000 

2.2361 

I.OOOO 

I-2599 
1.4422 

1.5874 
1.7100 

6 

7 
8 

9 
10 

36 
49 
64 
81 

I  OO 

216 

343 
5" 
729 

I  OOO 

2.4495 
2.6458 
2.8284 
3.0000 
3.1623 

1.8171 
1.9129 

2.OOOO 
2.O8OI 
2.1544 

ii 

12 
13 
14 
15 

I  21 

i  44 
i  69 
i  96 

2  25 

I  331 

I  728 

2  197 

2  744 
3  375 

3.3166 

3-4641 
3.6056 

3.7417 
3.8730 

2.2240 
2.2894 

2.3513 
2.4IOI 
2.4662 

16 

i7 
18 

19 

20 

2  56 
2  89 

3  24 

361 

4  oo 

4  096 
4  9*3 
5  832 
6  859 
8  ooo 

4.0000 

4.1231 
4.2426 
4.3589 
4.4721 

2.5198 

2.57J3 
2.6207 
2.6684 
2.7144 

21 
22 

23 
24 

25 

4  41 
4  84 
5  29 
5  76 
6  25 

9  261 

10  648 
12  167 
I3  824 

15  625 

4.5826 

4.6904 
4.7958 
4.8990 

5.0000 

2.7589 
2.8020 
2.8439 
2.8845 
2.9240 

26 

3 

29 
30 

6  76 
7  29 
7  84 
8  41 
9  oo 

16  576 
19683 

21  952 
24  389 

27  ooo 

5.0990 
5.1962 
5.2915 
5.3852 
5.4772 

2.9625 
3.0000 
3-0366 

3-0723 
3.1072 

31 
3* 
33 
34 
35 

9  61 
10  24 
10  89 
II  56 

12  25 

29  791 
32  768 

35  937 
39  304 

42  875 

5.5678 
5-6569 
5.7446 
5.8310 
5.9161 

3-I4I4 
3-1748' 
3-2075 
3.2396 
3.2711 

36 
37 
38 
39 
40 

12  96 
I3  69 

14  44 

15  21 

16  oo 

46  656 
5°  653 
54872 

59  3i9 

64  ooo 

6.OOOO 

6.0828 

6.1644 
6.2450 
6.3246 

3.3019 
3.3322 
3.3620 

3-3912 
3.4200 

4i 

42 

43 
44 
45 

16  81 
17  64 
18  49 
19  36 
20  25 

68  921 
74  088 
79  507 
85  184 
91  125 

6.4031 
6.4807 

6.5574 
6.6332 
6.7082 

3.4482 
3.4760 
3.5034 
3-53^3 
3.5569 

46 

47 
48 

49 
50 

21  l6 
22  09 
23  04 

24  01 
25  oo 

97  336 
103  823 
no  592 
117  649 
125  ooo 

6.7823 
6.8557 

6.9282 
7.0000 

7.0711 

3-5830 
3.6088 
3-6342 
3.6593 
3.6840 

TABLES  AND  MISCELLANEOUS  INFORMATION.  47* 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

51 
52 

53 
54 
55 

26  oi 

27  04 
28  09 

29  1  6 
30  25 

132  651 
140  6c8 
148  877 
157  464 
166  375 

7.1414 
7.2III 
7.2801 

70485 
7.4162 

3.7084 
3-7325 
3-7563 
3-7798 
3.8030 

56 

11 
£ 

3*  36 
32  49 
33  64 
34  81 
36  oo 

175  616 

185  193 
195  112 

205  379 
216  ooo 

7.4833 

ffi 

7.68II 
7.7460 

3-8259 
3.8485 
3.8709 
3:8930 

3-9  i  49 

61 

62 

63 
64 

65 

37  21 
38  44 
39  69 
40  96 
42  25 

226  981 
238  328 
250  047 
262  144 
274  625 

7.8lO2 
7.8740 

7-9373 
8.0000 
8.0623 

3-9365 
3-9579 
3-9791 

4.0000 
4.0207 

66 

67 
63 
69 
70 

43  56 
44  89 
46  24 
47  61 
49  oo 

287  496 
300  763 
314  432 
328  509 

343  °°° 

8.1240 
8.1854 
8.2462 
8.3066 
8.3666 

4.0412 
4.0615 
4.0817 
4.1016 
4.1213 

7i 

72 

73 
74 
75 

5°  4i 
5i  84 
53  29 
54  76 
56  25 

357  9n 
373  248 
389  017 
405  224 
421  875 

8.4261 

8.4853 
8.5440 
8.6023 
8.6603 

4.1408 
4.1602 
4-1793 
4.1983 
4,2172 

76 

77 
78 

79 

80 

57  76 

60  84 
62  41 
64  oo 

438  976 
456  533 
474  552 
493  °39 
512  ooo 

8.7178 
8.7750 
8.8318 
8.8882 
8.9443 

4.2358 
4.2543 
4.2727 
4.2908 
4.3089 

81 
82 
83 
84 

85 
86 

87 
88 
89 
90 

65  61 

67  24 
68  89 
70  56 
72  25 

531  44i 
55i  368 
57i  787 
592  704 
614  125 

9.0000 

9-°554 
9.1104 
9.1652 
9.2195 

4.3267 

4-3445 
4.3621 

tps 

73  96 
75  69 
77  44 
79  2I 
81  oo 

636  056 
658  5°3 
68  i  472 
704  969 
729  ooo 

9.2736 

9'3274 
9.3808 
9.4340 
9.4868 

4.4140 
4.4310 
4.4480 
4.4647 
4.4814 

9i 
92 

93 
94 
95 

82  81 
84  64 
8649 
88  36 
90  25 

753  571 
778  688 
804  357 
830  584 
857  375 

9-5394 
9-59*7 
9'6437 
9.6954 
9.7468 

4-4979 
4.5144 

4.5307 
4.5468 
4-5629 

96 
97 
98 
99 

100 

92  16 
94  09 
96  04 
98  oi 

I  OO  OO 

884  736 
912  673 
941  192 
970  299 

I  OOO  OOO 

9.7980 
9.8489 
9.8995 
9-9499 

IO.OOOO 

4-5789 
4-5947 
4.6104 
4.6261 
4.6416 

47s 


DRA  WING   AND    DESIGNING. 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

IOI 
1O2 
103 

104 
105 

O2  OI 
04  04 
06  09 

08  16 
10  25 

I  030  301 
I  06  I  208 
092  727 
124  864 
157  625 

10.0499 
10.0995 
10.1489 
10.1980 
10.2470 

4.6570 
4.6723 

4.6875 
4.7027 
4-7I77 

1  06 
107 

108 
109 
no 

12  36 

14  49 
16  64 
18  81 

21  OO 

191  016 
225  043 
259  712 
295  029 
331  ooo 

10.2956 
10.3441 
10.3923 
10.4403 
10.4881 

4.7326 

4-7475 
4.7622 
4.7769 
4.7914 

III 

112 

"3 
114 

TI5 

23  21 

25  44 

27  69 
29  96 

32  25 

367  631 
404  928 
442  897 
481  544 
520  875 

IO-5357 
10.5830 
10.6301 
10.6771 
10.7238 

4.8059 
4.8203 
4.8346 
4.8488 
4,8629 

116 
117 

its 

119 

1  20 

34  56 
3689 

39  24 
41  61 
44  oo 

560  896 
601  613 
643  032 
685  159 
728  ooo 

10.7703 
10.8167 
10.8628 
10.9087 
10.9545 

4.8770 
4.8910 
4.9049 
4.9187 
4.9324 

121 

122 
I23 
124 

I25 

46  41 
48  84 
5'  29 
53  76 
56  2S 

771  561 
815  848 
860  867 

906  624 
i  953  125 

11.0000 

11.0454 
11.0905 

".1355 
11.1803 

4.9401 
4-9597 
4-9732 
4.9866 
5.0000 

126 
127 
128 
I29 
I30 

58  76 
61  29 
63  84 
66  41 

69  oo 

2  OOO  376 
2  048  383 
2  097  152 
2  146  689 
2  197  OOO 

1  1.2250 
11.2694 
ii-3!37 
II.3578 
11.4018 

5-oi33 
5.0265 

5-0397 
5.0528 
5-0658 

131 
I32 

133 
134 
135 

71  61 

74  24 
7689 

79  S^ 
82  25 

2  248  091 
2  299  968 
2  352  637 
2  406  IO4 

2  460  375 

n-4455 
11.4891 
11.5326 

H.5758 
11.6190 

5.0788 
5.0916 

5-I045 
5.1172 

5-I299 

136 
137 
138 
139 

I4O 

84  96 
87  69 
90  44 
93  21 
96  oo 

2  5*5  456 

2  57i  353 

2  628  072 
2  685  619 

2  744  ooo 

11.6619 
11.7047 

11-7473 
11.7898 
11.8322 

5.1426 

S-lSSl 
5.1676 
5.1801 

5.1925 

141 
142 

H3 

144 

us 

i  98  81 

2  OI  64 

2  04  49 

2  07  36 
2  IO  25 

2  803  221 
2  863  288 
2  924  207 
2  985  984 

3  °48  625 

11.8743 
11.9164 
11.9583 

I2.OOOO. 
12.0416 

5.2048 
5.2171 
5-2293 
5-2415 
5-2536 

146 

147 

148 

149 

'5° 

2  13  16 

2  16  09 

2  I9  04 

2  22  OI 
2  25  OO 

3  112  136 
3  176  523 
3  241  792 
3  307  949 
3  375  ooo 

12.0830 
12.1244 
12.1655 
I2.2O66 
12.2474 

5.2656 
5.2776 
5.2896 

5-3015 
5-3I33 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION. 


Number 

|  •   Square. 

Cube. 

Square  Root. 

Cube  Root. 

'5« 

152 

153 
154 

'55 

2  28  OI 
2  31  04 

2  34  09 
2  37  16 

2  40  25 

3  442  951 
3  511  808 
3  58i  577 
3  652  264 
3  723  875 

12.2882 
12.3288 
12.3693 
12.4097 
12.4499 

5.3251 
5.3368 
S-3485 
5-360I 
5-37I7 

156 

'57 
158 

*59 
160 

2  43  36 
2  46  49 
2  49  64 
2  52  81 

2  56  OO 

3  796  416 
3  869  893 
3  944  312 
4  019  679 
4  096  ooo 

12.4900 
12.5300 
12.5698 
12.6095 
12.6491 

5-3832 

5-3947 
5.4061 

5-4288 

lOl 

162 

I3 
164 

165 

2  59  21 
2  62  44 

2  65  69 

2  68  96 

2  72  25 

4  '73  281 
4  251  528 

4  33°  747 
4  410  944 
4  492  125 

12.6886 
12.7279 
12.7671 
12.8062 
12.8452 

5.4401 

5-45H 
5.4626 

5-4737 
5.4848 

166 
167 
168 
169 
170 

2  75  56 

2  78  89 
2  82  24 

2  85  61 

2  89  OO 

4  574  296 
4  657  463 
4  74i  632 
4  826  809 
4  913  ooo 

12.8841 
12.9228 
12.9615 
13.0000 
13.0384 

5-4959 
5.5069 

5-5!78 
5.5288 
5-5397 

171 
172 

173 
174 
ITS 

2  92  41 

2  95  84  ' 
2  99  29 
3  02  76 
3  °6  25 

5  ooo  211 
5  088  448 
5  '77  7^7 
5  268  024 

5  359  375 

13.0767 
13.1149 
13.1529 
13.1909 
13.2288 

5-5505 
5-56I3 
5-5721 
5.5828 
5-5934 

170 

177 
178 

179 
180 

3  09  76 
3  '3  29 
3  '6  84 
3  20  41 
3  24  oo 

5  45'  776 
5  545  233 
5  639  752 
5  735  339 
5  832  ooo 

13.2665 
i3-304i 
I3-34I7 
I3-379I 
13.4164 

5.6041 

5.6i47 
5.6252 

5-6357 
5.6462 

181 
182 

183 
184 
185 

3  27  61 
3  3*  24 
3  34  89 
3  38  56 
3  42  25 

5  929  74i 
6  028  568 
6  128  487 
6  229  504 
6  331  625 

I3-4536 
13.4907 

I3-5277 
I3-5647 
13.6015 

5-6567 
5.6671 

56774 
5-6877 
5.6980 

1  86 
187 
1  88 
189 
190 

3  45  96 
3  49  69 
3  53  44 
3  57  21 
3  6  1  oo 

6  434  856 
6  539  203 
6  644  672 
6  751  269 
6  859  ooo 

136382 
13.6748 
i3-7"3 
13-7477 
13.7840 

5-7083 
5-7185 
5-7287 
5-7388 
5-7489 

191 
192 

193 
194 

T95 

3  64  81 
3  68  64 
3  72  49 
3  76  36 
3  80  25 

6  967  871 
7  077  888 
7  189  057 
7  301  384 
7  4i4  875 

13.8203 
13.8564 
13.8924 
13.9284 
13.9642 

5-759° 
5.7690 

5-7790 
5.7890 

5-7989 

196 
197 
198 
199 

200 

3  84  16 
3  88  09 
3  92  04 
3  96  oi 
4  oo  oo 

7  529  536 
7  645  373 
7  762  392 
7  880  599 
8  ooo  ooo 

14.0000 

14-0357 
14.0712 
14.1067 
14.1421   ! 

5.8088 
5.8186 
5.8285 

5-8383 
5.8480 

47! 


DRAWING   AND    DESIGNING. 


Number     Square. 

Cube. 

Square  Root. 

Cube  Root. 

201 

202 
203 
204 
205 

4  04  01 
4  08  04 
4  12  09 
4  16  16 
4  20  25 

8  120  601 
8  242  408 
8  365  427 
8  489  664 
8  615  125 

14.1774 
14.2127 
14.2478 
14.2829 
14.3178 

5.8578 
5.8675 
5-877I 
5.8868 
5.8964 

206 
207 
208 
209 
210 

4  24  36 
4  28  49 
4  32  64 
4  36  81 
4  41  oo 

8  741  816 
8  869  743 
8  998  912 

9  I29  329 
9  261  ooo 

14.3527 

I4-3875 
14.4222 

14.4568 
14.4914 

5.9059 
5-9I55 
5.9250 

5-9345 
5-9439 

211 

212 
213 
214 
2I5 

4  45  21 
4  49  44 
4  53  69 
4  57  96 
4  62  25 

9  393  93i 
9  528  128 

9  663  597 
9  800  344 

9  938  375 

14.5258 
14.5602 

14-5945 
14.6287 
14.6629 

5-9533 
5-9627 
5-9721 
5.9814 
5.9907 

216 

217 

218 
219 

220 

4  t>6  56 
4  70  89 
4  75  24 
4  79  61 
4  84  oo 

10  077  696 
10  218  313 
10  360  232 

10  503  459 
10  648  oco 

14.6969 
14.7309 
14.7648 
14.7986 
14.8324 

6.0000 
6.0092 
6.0185 
6.0277 
6.0368 

221 
222 
223 
224 
225 

4  8*  41 
4  92  84 
4  97  29 
5  01  76 
5  06  25 

10  793  861 
10  941  048 
i  i  089  567 
ii  239  424 
ii  390  625 

14.8661 
14.8997 

14-9332 
14.9666 
1  5.0000 

6.0459 
6.0550 
6.0641 
6.0732 
6.0822 

226 
227 
228 

229 
2^0 

5  10  76 
5  IS  29 
5  19  84 
5  24  41 
5  29  oo 

ii  543  !/6 
ii  697  083 
ii  852  352 

12  OO8  989 
12  167  OOO 

15.0333 
1  5.0665 
15.0997 

IS-1  327 
15.1658 

6.0912 

6.1002 

6.1091 
6.1180 
6.  1  269 

23I 

232 

233 
234 

23S 

5  33  61 
5  38  24 

5  42  89 
5  47  56 

5  52  25 

12  326  391 

12  487  168 
12  649  337 

12  Si  2  904 

12  977  875 

15.1987 

15-2315 
15.2643 

i5-297i 
i5-3297 

6.1358 
6.1446 

6.1534 
6.1622 
61710 

236 
237 
238 
239 
240 

5  5696 
S6i  69 

5  66  44 
5  7i  21 
5  76  oo 

13  144  256 

13  312  053 
13  481  272 
13  651  919 
13  824  ooo 

15-3623 
15-3948 
15.4272 
I5-4596 
154919 

6.1797 
6.1885 
6.1972 
6.2058 
6.2145 

241 
242 

243 
244 

245 

5  80  81 
5  85  64 
5  9°  49 
5  95  36 
6  oo  25 

13  997  52i 
14  172  488 
14  348  907 
14  526  784 
14  706  125 

15.5242 

15-5563 
15.5885 
15.6205 
15-6525 

6.2231 
6.2317 
6.2403 
6.2488 
6.2573 

246 
247 
248 

249 

250 

6  05  16 
6  10  09 
6  15  04 
6  20  01 
6  25  oo 

14  886  936 
15  069  223 
15  252  992 
15  438  249 
.  15  625  ooo 

15.6844 
15.7162 

15.7480 

15.7797 
15.8114 

6.2658 
6.2743 
6.2828 
6.2912 
6.2996 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  47* 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

251 
252 

253 
254 
255 

6  30  01 

6  35  °4 
6  40  09 
6  45  16 
6  50  25 

I5  813  251 

16  003  008 
16  194  277 
16  387  064 
16  581  375 

15.8430 
15.8745 
15.9060 

15-9374 
15.9687 

6.3080 
6.3164 
6.3247 
6.3330 
6.3413 

256 

257 
258 
259 
260 

6  55  36  . 
6  60  49 
6  65  64 
6  70  81 
6  76  oo 

16  777  216 
16  974  593 
17  173  512 

17  373  979 
17  576  ooo 

I6.OOOO 
16.0312 
16.0624 
16.0935 
16.1245 

6.3496 

6-3579 
6.3661 

6-3743 
6.3825 

26l 
262 
263 
264 
265 

6  JJl  21 

6  86  44 
6  91  69 
6  96  96 
7  02  25 

17  779  581 
17  984  728 
18  191  447 
i  8  399  744 
18  609  625 

16.1555 
16.1864 
16.2173 
16.2481 
16.2788 

6.3907 
6.3988 
6.4070 
6.4151 
6.4232 

266 
267 
268 
269 
270 

7  07  56 
7  12  89 
7  18  24 
7  23  61 
7  29  oo 

18  821  096 
19  034  163 
19  248  832 
19  465  109 
19  683  ooo 

16.3095 
16.3401 
16.3707 
16.4012 
16.4317 

6.4312 
6.4393 
6.4473 
<M553 
6.4633 

271 
272 
273 
274 
275 

7  34  4i 
7  39  84 

7  45  29 
7  5°  76 
7  56  25 

19  902  511 

2D  123  648 
20  346  417 
20  570  824 
20  796  87  S 

16.4621 
16.4924 
16.5227 
16.5529 
16.5831 

6.4713 
6.4792 
6.4872 
6.4951 
6.  5030 

276 
277 
278 

279 
280 

7  61  76 
7  67  29 

7  7^  84 
7  78  41 
7  84  oo 

21  O24  576 

21  253  933 

21  484  952 
21  717  639 
21  952  000 

16.6132 
16.6433 
16.6733 
16.7033 
16.7332 

6.5108 
6.5187 
6.5265 

6.5343 
6.5421 

28l 
282 

**3 
284 
285 

7  89  61 

7  95  24 
8  oo  89 
8  06  56 
8  12  25 

22  l88  041 
22  425  768 
22  665  187 
22  906  304 
23  I49  I25 

16.7631 
16.7929 
16.8226 
16.8523 
16.8819 

6.5499 
6-5577 
6.5654 
6-5731 
6.5808 

286 

287 
288 
289 
290 

8  17  96 
8  23  69 
8  29  44 
8  35  21 
8  41  oo 

23  393  656 
23  639  903 
23  887  872 

24  137  569 
24  389  ooo 

16.9115 
16.9411 
16.9706 
17.0000 
17.0294 

6.5885 
6.5962 
6.6039 
6.6115 
6.6191 

291 
292 

293 
294 

295 

8  46  Si 
8  52  64 
8  5849 
8  64  36 
8  70  25 

24  642  171 
24  897  088 

25  *53  757 
25  412  184 

25  672  375 

17.0587 
17.0880 
17.1172 
17.1464 
17.1756 

6.6267 
6.6343 
6.6419 
6.6494 
6.6569 

296 
297 
298 

299 

300 

8  76  16 
8  82  09 
8  88  04 
8  94  01 
9  oo  oo 

25  934  336 
26  198  073 
26  463  592 
26  730  899 
27  ooo  ooo 

17.2047 

17.2337 
17.2627 
17.2916 

17.3205 

6.6644 
6.6719 
6.6794 
6.6869 
6.6943 

47' 


DRAWING  AND    DESIGNING. 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

3OI 
302 
303 
304 
305 

9  06  01 
9  12  04 
9  18  09 
9  24  16 
9  30  25 

27  270  901 

27  543  608 
27  818  127 
28  094  464 
28  372  625 

17-3494 
I7-378I 
17.4069 

17.4356 
17.4642 

6.7018 
6.7092 
6.7166 
6.7240 
6.7313 

306 

307 
308 

3°9 
310 

9  36  36 
9  42  49 
9  48  64 
9  54  81 
9  61  oo 

28  652  616 

28  934  443 
29  218  112 
29  503  629 
29  791  ooo 

17.4929 

I7-52I4 
17.5499 

I7-5784 
17.6068 

6.7387 
6.7460 

6-7533 
6.7606 
6.7679 

CO  CO  CO  CO  CO 
l/i  4*-  Co  to  1-1 

9  67  21 

9  73  44 
9  79  69 
9  85  96 

9  92  25 

30  080  231 
30  371  328 
30  664  297 
30  959  144 
3i  255  875 

J7-6352 

17.6918 
17.7200 
17.7482 

6.7752 
6.7824 
6.7897 

6-7969 
6.8041 

320 

998  56 
10  04  89 
10  ii  24 
10  17  61 
10  24  oo 

31  554  496 
3i  855  013 
32  157  432 
32  461  759 
32  768  ooo 

17.7764 
17.8045 
17.8326 
17.8606 
17.8885 

6.8113 
6.8185 
6.8256 
6.8328 
6.8399 

321 
322 
323 
324 
325 

10  30  41 
10  36  84 
10  43  29 
10  49  76 
10  56  25 

33  076  161 
33  386  248 
33  698  267 
34  012  224 
34  328  125 

17.9165 
17.9444 
17.9722 
18.0000 
18.0278 

6.8470 
6.8541 
6.8612 
6.8683 

6.8753 

Co  CO  CO  CO  Co 
Co  to  to  to  to 
O  VO  OO^J  ON 

10  62  76 
10  69  29 
10  75  84 
10  82  41 
10  89  oo 

34  645  976 

34  965  783 
35  287  552 
35  611  289 
35  937  ooo 

18.0555 
18.0831 
18.1108 
18.1384 
18.1659 

6.8824 
6.8894 
6.8964 

6.9034 
6.9104 

33  * 
332 
333 
334 

335 

10  95  61 
ii  02  24 
ii  08  89 
ii  15  56 

II  22  25 

36  264  691 
36  594  368 
36  926  037 
37  259  704 
37  595  375 

18.1934 
18.2209 
18.2483 
18.2757 
18.3030 

6.9174 
6.9244 

6-93'3 
6.9382 
6.9451 

336 
337 
338 
339 
340 

II  28  96 

ii  35  69 
ii  42  44 
ii  49  21 
ii  56  oo 

37  933  056 
38  272  753 
38  614  472 
38  958  219 
39  304  ooo 

18.3303 
18.3576 
18.3848 
18.4120 
18.4391 

6.9521 
6.9589 
6.9658 
6.9727 
6-9795 

342 
343 
344 
345 

ii  62  81 
ii  69  64 
ii  76  49 
ii  83  36 
ii  90  25 

39  651  821 
40  ooi  688 
40  353  607 
40  707  584 
41  063  625 

18.4662 
18.4932 
18.5203 
18.5472 
18.5742 

6.9864 

6.9932 
7.0000 
7.0068 
7.0136 

346 
347 
348 
349 
350 

ii  97  16 
12  04  09 
12  ii  04 

12  l8  01 
12  25  00 

41  421  736 
41  781  923 
42  144  192 
42  508  549 
42  875  ooo 

18.6011 
18.6279 
18.6548 
18.6815 
18.7083 

7.0203 
7.0271 

7-0338 
7.0406 

7.0473 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION. 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

351 
352 

353 
354 
355 

12  32  01 

12  39  04 

12  46  09 

12  53  16 

12  60  25 

43  243  55i 
43  614  208 

43  986  977 
44  361  864 
44  738  875 

I8.7350 
18.7617 
18.7883 
18.8149 

18.8414 

7.0540 
7.0607 
7.0674 
7.0740 
7.0807 

356 
357 
358 
359 
360 

12  67  36 

12  74  49 
12  81  64 
12  88  81 
12  96  oo 

45  118  016 
45  499  293 
45  882  712 
46  268  279 
46  656  ooo 

18.8680 
18.8944 
18.9209 
18.9473 
18.9737 

7-0873 
7.0940 
7.IOO6 
7.1072 
7.1138 

36< 
362 

363 
364 
365 

13  03  21 

13  10  44 
13  17  69 
13  24  96 
13  32  25 

47  045  88  i 
47  437  928 
47  832  147 
48  228  544 
48  627  125 

I9OOOO 
19.0263 
19.0526 
19.0788 
19.1050 

7.1204 
7.1269 

7.1335 
7.1400 
7.1466 

366 
367 

3S 
369 

370 

!3  39  56 
13  46  89 

13  54  24 
13  61  61 
13  69  oo 

49  027  896 
49  43°  863 
49  836  032 
50  243  409 
50  653  ooo 

19.1311 
19.1572 
19-1833 
19.2094 
19.2354 

7.I53I 
7'  '596 
7.I66I 
7.1726 
7.I79I 

37i 
372 
373 
374 

375 

13  76  41 
13  83  84 
13  91  29 
13  98  76 
14  06  25 

51  064  81  i 
51  478  848 
51  895  117 
52  3i3  624 

52  734  375 

19.2614 
19.2873 
19.3132 

19-339  r 
19.3649 

7.1855 
7.1920 
7.1984 
7.2048 
7.2II2 

376 
377 
378 

379 
380 

H  *3  76 

14  21  29 
14  28  84 
14  36  41 

14  44  oo 

53  157  376 
53  582  633 
54  oio  152 

54  439  939 
54  872  ooo 

19.3907 
19.4165 
19.4422 
19.4679 
19.4936 

7.2177 
7.2240 
7.2304 
7.2368 
7.2432 

38i 
382 
383 
384 
385 

14  51  61 
14  59  24 
14  66  89 

H  74  56 

14  82  25 

55  306  341 
55  742  968 
56  181  887 
56  623  104 
57  066  625 

19.5192 
19.5448 
19.5704 

19-5959 
19.6214 

7.2495 
7.2558 
7.2622 
7.2685 
7.2748 

3«6 
387 
388 
389 
390 

14  89  96 
14  97  69 
15  05  44 
IS  13  21 

15  21  OO 

57  512  456 
57  960  603 
58  411  072 
58  863  869 
59  319  ooo 

19.6469 
19.6723 
19.6977 
19.7231 
19.7484 

7.2811 

7.2874 
7.2936 
7.2999 
7.^061 

39i 
392 
393 
394 
395 

15  28  81 
15  36  64 

15  44  49 

15  52  36 
15  60  25 

59  776  471 
60  236  288 
60  698  457 
61  162  984 
61  629  875 

19-7737 
19.7990 
19.8242 
19.8494 
19.8746 

7-3I24 
7.3186 
7.3248 
7.33'o 
7.3372 

396 

397 
398 
399 

400 

15  6S  16 
15  76  09 
15  84  04 
15  92  01 
16  oo  oo 

62  099  136 
62  570  773 
63  044  792 
63  521  199 
64  ooo  ooo 

19.8997 
19.9249 

19.9499 
19.9750 
20.0000 

7-3434 
7.3496 
7.3558 
7.3619 
7.3681 

47" 


DRAWING   AND   DESIGNING. 


Number 

Square. 

Cube. 

Square  Root. 

Cuba  Root. 

401 
402 

403 
404 

405 

16  08  oi 
16  16  04 
16  24  09 
16  32  16 
i  6  40  25 

64  481  201 
64  964  808 
65  450  827 

65  939  264 
66  430  125 

20.0250 
20.0499 

20.0749 
20.0998 
20.1246 

7-3742 
7.3803 
7.3864 

7.3925 
7.3986 

406 
407 
408 
409 
410 

16  48  36 
16  56  49 
16  64  64 
16  72  81 
16  8  i  oo 

66  923  416 
67  419  143 
67  917  312 
68  417  929 

68  921  ooo 

20.1494 
20.1742 
20.1990 
20.2237 
20.2485 

7.4047 
7.4108 
7.4169 
7.4229 
7.4290 

411 
413 

413 
414 

415 

16  89  21 
16  97  44 
17  05  69 
17  13  96 
17  22  25 

69  426  531 
69  934  528 
70  444  997 
70  957  944 
7i  473  375 

20.2731 
20.2978 
20.3224 
20.3470 
20.3715 

7-435° 
7.4410 

7.4470 
7.4530 

7-459° 

4l6 

417 
4l8 
419 

420 

17  30  56 
17  38  89 
17  47  24 
17  55  61 
17  64  oo 

71  991  296 
72  511  713 
73  °34  632 
73  56°  °59 

74  088  ooo 

20.3961 
20.4206 
20.4450 
20.4695 
20.4939 

7.4650 
7.4710 
7.4770 
7.4829 
7.4889 

42  £ 
422 

423 
424 

425 

17  72  41 
17  80  84 
17  89  29 

17  97  76 
18  06  25 

74  618  461 
75  I5I  448 
75  686  967 
76  225  024 
76  765  625 

20.5183 
20.5426 
20.5670 
20.5913 
20.6155 

7.4948 
7.5007 
7.5067 
7.5126 

7.5185 

426 
427 
428 
429 

43° 

18  14  76 
18  23  29 
18  31  84 
18  40  41 
18  49  oo 

77  3°8  776 
77  854  483 
78  402  752 

78  953  589 
79  507  ooo 

20.6398 
20.6640 
20.6882 
20.7123 
20.7364 

7.5244 
7.53°2 
7.5361 
7.5420 
7.5478 

431 
432 
433 
434 

435 

18  57  61 
18  66  24 
18  74  89 
18  83  56 
18  92  25 

80  062  991 
80  621  568 
81  182  737 
8  i  746  504 
82  312  875 

20.7605 
20.7846 
20.8087 
20.8327 
20.8567 

7.5537 
7-5595 
7.5654 

7-5712 
7-577° 

436 

438 
439 
440 

19  oo  96 
19  09  69 
19  18  44 

19  27  21 

19  36  oo 

82  881  856 

83  453  453 
84  027  672 
84  604  519 

85  184  ooo 

20.8806 
20.9045 
20.9284 
20.9523 
20.9762 

7.5828 
7.5886 

7-5944 
7.6001 
7-6059 

441 
442 
443 
444 

445 

19  44  81 

19  53  64 
19  62  49 
19  71  36 

19  80  25 

85  766  121 

86  350  888 
86  938  307 
87  528  384 
88  121  125 

21.0000 
21.0238 
2I.O476 
21.0713 
2I.O95O 

7.6117 
7.6174 
7.6232 
7.6289 
7.6346 

446 

447 
448 

449 
450 

19  89  16 
19  98  09 

20  07  04 
20  l6  01 

20  25  oo 

88  716  536 
89  314  623 

89  9l$  392 
90  518  849 
91  125  ooo 

2I.II87 
21.1424 
21.  l66o 
21.1896 
21.2132 

7.6403 
7.6460 
7-6517 
7.6574 
7-6631 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  47 


Numbe 

Square. 

.  Cube. 

Square  Root. 

Cube  Root. 

45' 

452 

453 
454 

455 

20  34  01 
20  43  04 
20  52  09 
20  61  16 
20  70  25 

91  733  85* 
92  345  4o8 
92  959  677 
93  576  664 
94  196  375 

21.2368 
21.2603 
21.2838 
21.3073 
21.3307 

7.6688 
7.6744 
7.6801 

7.6857 
7.6914 

456 
457 
458 
459 
460 

20  79  36 
20  88  49 
20  97  64 
21  06  81 

21  l6  00 

94  818  816 

95  443  993 
96  071  912 
96  702  579 
97  336  ooo 

21.3542 
21.3776 
21.4009 
21.4243 
21.4476 

7.6970 
7.7026 
7.7082 
7.7138 
7.7194 

461 
462 

463 
464 
465 

21  25  21 

21  34  44 
21  43  69 

21  52  96 
21  62  25 

97  972  181 
98  611  128 
99  252  847 

99  897  344 
100  544  625 

21.4709 
21.4942 
21.5174 
21.5407 
21.5639 

7.7250 
7.7306 
7.7362 
7.7418 
7-7473 

466 
467 
468 
469 

470 

21  71  56 
21  80  89 
21  90  24 

21  99  61 

22  09  OO 

101  194  696 

i  01  847  563 

102  503  232 

103  161  709 

103  823  ooo 

21.5870 
2I.6I02 
21.6333 
21.6564 
21.6795 

7.7539 
7.7584 
7.7639 
7.7695 
7.7750 

47i 
472 
473 
474 

475 

22  l8  41 
22  27  84 

22  37  29 

22  46  76 
22  56  25 

104  487  III 
105  154  048 

105  823  817 

106  496  424 
107  171  875 

21.7025 
21.7256 
21.7486 
21.7715 
21-7945 

7.7805 
7.7860 

7.7915 

7.7970 
7.8025 

476 
477 
478 

479 
480 

22  65  76 

22  75  29 

22  84  84 

22  94  41 
23  04  oo 

107  850  176 

i°8  531  333 
109  215  352 
109  902  239 
no  592  ooo 

21.8174 
21.8403 
21.8632 
2I.886I 
21.9089 

7.8079 

7.8I34 
7.8188 
7.8243  - 
7.8297 

481 
482 
483 
484 
485 

23  13  61 
23  23  24 
23  32  89 
23  42  56 
23  52  25 

III  284  641 
iii  980  168 
112  678  587 

"3  379  9°4 
114  084  125 

21.9317 
21.9545 
21.9773 
22.0000 
22.0227 

7.8352 
7.8406 
7.8460 

7.8514 
7.8568 

486 

487 
488 
489 
490 

23  61  96 
23  71  69 
23  81  44 
23  91  21 
24  01  oo 

114  791  256 
115  501  303 
116  214  272 
116  930  169 
117  649  ooo 

22.0454 
22.0681 
22.0907 
22.1133 
22.1359 

7.8622 
7.8676 
7.8730 
7.8784 
7.8837 

491 
492 
493 
494 
495 

24  10  81 
24  20  64 
24  30  49 
24  40  36 
24  50  25 

118  370  771 
119  095  488 
119  823  157 
120  553  784 
121  287  375 

22.1585 
22.l8l  I 
22.2036 
22.2261 
22.2486 

7.889I 
7.8944 
7.8998 
7.9051 
7.9105 

496 

497 
498 

499 

500 

24  60  16 
24  70  09 
24  80  04 
24  90  01 
25  oo  oo 

122  023  936 
122  763  473 
123  505  992 
124  251  499 
125  ooo  ooo 

22.2711 
22.2935 
22.3159 
22.3383 
22.3607 

7.9158 
7.9211 
7.9264 

7-93I7 
7.9370 

47" 


DRAWING  AND    DESIGNING. 


'Number;     Square. 

Cube.           Square  Root. 

Cube  Root. 

501 

502 

503 
504 
505 

25  10  01 

25  20  04 
25  30  09 

25  40  16 
25  50  25 

125  751  501 
126  506  008 
127  263  527 
128  024  064 
128  787  625 

22.3830 
22.4054 
22.4277 
22.4499 
22.4722 

7.9423 
7.9476 
7.9528 
7-958I 

7-9634 

506 

507 
508 

5°9 
5io 

25  60  36 

25  70  49 
25  80  63 
25  90  8  i 
26  o  i  oo 

129  554  216 

130  323  843 
131  096  512 
131  872  229 
132  651  ooo 

22.4944 
22.5167 
22.5389 
22.5610 
22.5832 

7.9686 

7-9739 
7.9791 

7-9843 
7.9896 

511 
512 

5*3 

5M 
5i5 

26  II  21 

26  21  44 
26  31  69 
26  41  96 

26  52  25 

133  432  831 
134  217  728 
135  005  697 

!35  796  744 
136  590  875 

22.6053 
22.6274 
22.6495 
22.6716 
22.6936 

7-9948 
8.0000 
8.0052 
8.0104 
8.0156 

516 

5«7 
518 

5'9 

520 

26  62  56 
26  72  89 
26  83  24 
26  93  61 
27  04  oo 

137  388  096 
138  i  88  413 
138  991  832 

139  798  359 
140  608  ooo 

22.7156 
22.7376 
22.7596 
22.7816 
22.8035 

8.0208 
8.0260 
8.0311 
8.0363 
8.0415 

& 

522 
523 
524 
525 

27  H  4i 
27  24  84 
27  35  29 
27  45  76 
27  56  25 

141  420  761 
142  236  648 

143  055  667 
143  877  824 
144  703  125 

22.8254 
22.8473 
22.8692 
22.8910 
22.9129 

8.0466 
8.0517 
8.0569 
8.0620 
8.0671 

526 

527 
528 

529 

530 

27  66  76 
27  77  29 
27  87  84 
27  98  41 
28  09  oo 

MS  531  576 
146  363  183 
147  197  952 
148  035  889 
148  877  ooo 

22.9347 
22.9565 
22.9783 
23.0000 
23.0217 

8.0723 
8.0774 
8.0825 
8.0876 
8.0927 

53i 
532 
533 
534 
535 

28  19  61 
28  30  24 
28  40  89 
28  51  56 
28  62  25 

149  721  291 
150  568  768 

IS1  4i9  437 
152  273  304 

T53  13°  375 

23-0434 
23.0651 
23.0868 
23.1084 
23.1301 

8.0978 
8.1028 
8.1079 
8.1130 
8.1  180 

53<> 
537 
538 
539 
540 

28  72  96 
28  83  69 
28  94  44 

29  05  21 

29  16  oo 

*53  99°  656 
154  854  153 
155  720  872 
156  590  819 
157  464  ooo 

23-i5'7 

23-I733 
23.1948 
23.2164 
23.2379 

8.1231 
8.1281 
8.1332 
8.1382 

8-1433 

54i 
542 
543 
544 
545 
546 
547 
548 
549 
550 

29  26  81 
29  37  64 
29  48  49 

29  59  36 
29  70  25 

158  340  421 
159  220  088 
i  60  103  007 
160  989  184 
161  878  625 

23-2594 
23.2809 
23.3024 
23-3238 
23-3452 

8.1483 
8.1533 
8.1583 
8.1633 
8.1683 

29  81  16 
29  92  09 
30  03  04 
30  14  oi 
30  25  oo 

162  771  336 
163  667  323 
164  566  592 
165  469  149 
i  66  375  ooo 

23.3666 
23.3880 
23.4094 
23.4307 
23-4521 

8-1733 
8.1783 
8.1833 
8.1882 
8.1932 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  47 


12 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

551 

552 

553 
554 
555 

30  36  oi 

30  47  04 

30  58  09 

30  69  16 

30  80  25 

167  284  151 

168  196  608 
169  112  377 
170  031  464 
I    170  953  875 

23-4734 
23.4947 
23.5160 
23-5372 
23-5584 

8.1982 
8.2031 

8.  208  1 
8.2130 
8.2180 

556 
557 
558 
559 
560 

30  91  36 
31  02  49 

31  13  64 
31  24  81 
31  36  oo 

171  879  616 
172  808  693 
173  741  112 
174  676  879 
175  616  ooo 

23-5797 
23.6008 
23.6220 

23.6432 
23.6643 

8.2229 
8.2278 
8.2327 

8-2377 
8.2426 

56i 
562 

5*3 
564 

565 

31  47  21 

31  58  44 
31  69  69 
31  80  96 
31  92  25 

176  558  481 
177  504  328 

*78  453  547 
179  406  144 
180  362  125 

23.6854 
23-7065 
23.7276 

23.7487 
23.7697 

8.2475 
8.2524 
8.2573 
8.2621 
8.2670 

566 
567 
568 

569 
570 

32  03  56 
32  14  89 
32  26  24 
32  37  61 
32  49  oo 

18  i  321  496 
182  284  263 
183  250  432 
184  230  009 
185  193  ooo 

23.7908 
23.8118 
23.8328 
23.8537 
23.8747 

8.2719 
8.2768 
8.2816 
8.2865 
8.2913 

57i 
572 
573 
574 
575 

32  oo  41 
32  71  84 
32  83  29 
32  94  76 
33  06  25 

186  169  411 
187  149  248 
188  132  517 
189  119  224 
190  109  375 

23.8956 
23.9165 
23-9374 
23-9583 
23.9792 

8.2962 
8.3010 
8.3059 
8.3107 
8.3155 

576 
577 
573 

579 
580 

33  17  76 
33  29  29 
33  40  84 
33  52  41 
33  64  oo 

191  IO2  976 

192  100  033 

!93  I0°  SS2 
194  104  539 

195  112  OOO 

24.OOOO 
24.0208 
24.0416 
24.0624 
24.0832 

8.3203 
8.3251 

8-330° 
8.3348 
8.3396 

58< 

582 

583 
584 
585 

33  75  61 
33  87  24 
33  98  89 
34  10  56 

34  22  25 

196  122  941 

i97  i37  368 
198  155  287 
199  176  704 
200  20  i  625 

24.1039 
24.1247 
24.1454 

24.  1  66  1 
24-1868 

8.3443 
8.3491 

8-3539 
8.3587 
8.3634 

586 

587 
588 

589 
590 

34  33  96 
34  45  69 
34  57  44 
34  69  21 
34  8  i  oo 

2OI  230  056 
2O2  262  003 
203  297  472 
204  336  469 

205  379  00° 

24.2074 
24.2281 
24.2487 
24.2693 
24.2899 

8.3682 
8.3730 

8-3777 
8.3825 
8.3872 

59  i 
592 
593 
594 
595 

34  92  81 
35  04  64 

35  l6  49 
35  28  36 
35  40  25 

206  425  071 
207  474  688 
208  527  857 
209  584  584 

210  644  875 

24.3105 

24-33" 
24.3516 
24.3721 
24.3926 

8.3919 
8.3967 
8.4014 
8.4061 
8.4108 

596 
597 
598 

35  52  16 
35  64  09 
35  76  04 
35  88  oi 
36  oo  oo 

211  708  736 
212  776  173 
213  847  192 

214  921  799 
216  ooo  ooo 

24.4131 

24.4336 
24.4540 
24.4745 
24.4949 

».4i55 
8.4202 
8.4249 
8.4296 
8-4343 

4;13 


DRAWING   AND   DESIGNING. 


Number]     Square.             Cube.           Square  Koot.     Cube  Root. 

60  1 
602 
603 
604 
605 

36  12  OI 
36  24  04 
36  36  09 

36  48  16 
36  60  25 

217  08  i  801 
218  167  208 
219  256  227 

220  348  864 

221  445  I25 

24-5  '53 
24-5357 
24.5561 
24.5764 
24.5967 

8.4390 

8-4437 
8.4484 
8.4530 
8.4577 

606 
607 
608 
609 

610 
611 
612 
613 
614 
615 

36  72  36 
36  84  49 
36  96  64 
37  08  81 
37  21  oo 

222  545  016 
223  648  543 
224  755  7i2 
225  866  529 
226  981  ooo 

24.6171 
24.6374 

24-6577 
24.6779 
24.6982 

8.4623 
8.4670 
8.4716 
8.4763 
8.4809 

37  33  21 
37  45  44 
37  57  69 
37  69  96 
37  82  25 

228  099  131 

229  220  928 

23°  346  397 
231  475  544 
232  608  375 

24.7184 
24.7386 
24.7588 
24.7790 
24.7992 

8.4856 
8.4902 
8.4948 
8.4994 
8.5040 

616 
617 
618 
619 
620 

37  94  56 
38  06  89 
38  19  24 
38  31  61 
38  44  oo 

233  744  896 
234  885  113 
236  029  032 
237  176  659 
238  328  ooo 

24.8193 

24.8395 
24.8596 
24.8797 
24.8998 

8.5086 
8.5132 
8.5178 
8.5224 
8.5270 

621 
622 
623 
624 
625 

38  S6  4i 
38  68  84 
38  81  29 
38  93  76 
39  06  25 

239  483  061 
240  641  848 
241  804  367 
242  970  624 
244  140  625 

24.9199 

24.9399 
24.9600 
24.9800 
25.0000 

8-53'6 
8.5362 
8.5408 

8-5453 
8.5499 

626 
627 
628 
629 

630 

39  i»  76 
39  31  29 
39  43  84 
39  56  41 
39  69  oo 

i  245  3H  376 
246  491  883 
247  673  152 
'248  858  189 
'  250  047  ooo 

25.0200 
25.0400 
25.0599 
25.0799 
25.0998 

8-5544 
8.5590 

8-5635 
8.5681 
8.5726 

631 
632 

633 

634 
635 

39  8  i  61 
39  94  24 
40  06  89 
40  19  56 
40  32  25 

,  251  239  591 
252  435  968 
253  636  137 
254  840  104 
256  047  875 

25.1197 
25.1396 

25.1595 
25.1794 

25.1992 

8.5772  " 
8.5817 
8.5862 
8.5907 
8.5952 

636 

637 
638 

639 
640 

40  44  96 
40  57  69 
40  70  44 

4O  83  21 

40  96  oo 

257  259  456 
258  474  853 
259  694  072 
260  917  119 
262  144  ooo 

25.2190 
25.2389 

25-2587 
25.2784 
25.2982 

8-5997 
8.6043 
8.6088 
8.6132 
8.6177 

641 
642 

643 
644 

645 

41  08  81 

41  21  64 

4i  34  49 
41  47  36 
41  60  25 

263  374  721 
264  609  288 
265  847  707 
267  089  984 
268  336  125 

25.3180 
25-3377 
25-3574 
25.3772 
25-3969 

8.6222 
8.6267 
8.6312 
8.6357 
8.6401 

646 
647 
648 

649 
650 

41  73  16 
41  86  09 
41  99  04 

42  12  OI 

42  25  oo 

269  586  136 
270  840  023 
272  097  792 

273  359  549 
274  625  ooo 

25.4165 
25.4362 
25.4558 
25.4755 

2f>  4QCI 

8.6446 
8.6490 

8.6535 
8.6579 
8.6624 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  4/u 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

*5' 
652 

653 
654 
655 

42  38  oi 

42  51  04 
42  64  09 

42  77  16 
42  90  25 

275  894  45* 
277  167  808 
278  445  077 
279  726  264 
281  on  375 

25.5M7 
25-5343 
25.5539 
25-5734 
25.5930 

8.6668 
8.6713 
8-6757 
8.6801 
8.6845 

656 
657 
658 

file9 

43  °3  36 
43  l6  49 
43  29  64 
43  42  81 
43  S6  °° 

282  300  416 

283  593  393 
284  890  312 
286  191  179 
287  496  ooo 

25.6125 
25.6320 

25.6515 
••5.6710 
256905 

8.6890 
8.6934 
8.6978 
8.7022 
8.7066 

66  1 
662 
663 
664 
665 

43  69  21 
43  82  44 
43  95  69 
44  08  96 
44  22  25 

288  804  781 

290  117  528 
291  434  247 

292  754  944 
294  079  625 

25.7099 
25.7294 
25.7488 
25.7682 
25.7876 

8.7110 
8.7154 
8.7198 
8.7241 
8.7285 

666 
667 
668 
.669 
670 

44  35  56 
44  48  89 
44  62  24 

44  75  61 
44  89  oo 

295  408  296 
296  740  963 
298  077  632 
299  4i8  309 
300  763  ooo 

25.8070 
25.8263 

25.8457 
25.8650 
25.8844 

8.7329 
8-7373 
8.7416 
8.7460 

8.75°3 

671 
672 

673 
674 

^75 

45  °2  4i 
45  '5  84 
45  29  29 
45  42  76 
45  56  25 

302  III  711 

303  464  448 

304  821  217 
306  182  024 

307  546  875 

25.9037 
25.9230 
25.9422 
25.9615 
25.9808 

8-7547 
8.7590 
8.7634 
8.7677 
8.7721 

676 

677 
678 
679 
680 

45  69  76 
45  83  29 
45  96  84 
46  10  41 
46  24  oo 

308  915  776 

310  288  733 
311  665  752 
313  046  839 
314  432  ooo 

26.OOOO 
26.0192 
26.0384 
26.0576 
26.0768 

8.7764 
8.7807 
8.7850 
8.7893 
8.7937 

63  1 
682 
683 
684 
685 

46  37  61 
46  51  24 
46  64  89 
46  78  56 
46  92  25 

315  821  241 
317  214  568 
318  61  i  987 
320  013  504 
321  419  125 

26.0960 
26.1151 
26.1343 
26.1534 

26.1725 

8.7980 
8.8023 
8.8066 
8.8109 
8.8152 

686 
687 
688 
689 
690 

47  05  96 
47  19  69 
47  33  44 
47  47  21 
47  61  oo 

322  828  856 
324  242  703 
325  660  672 
327  082  769 
328  509  ooo 

26.1916 
26.2107 
26.2298 
26.2488 
26.2679 

8.8194 
8.8237 
8.8280 
8.8323 
8.8366 

09  1 

692 

693 
694 
695 

47  74  81 
47  88  64 
48  02  49 
48  16  36 
48  30  25 

329  939  37i 
33i  373  888 
332  812  557 
334  255  384 
335  702  375 

26.2869 
26.3059 
26.3249 

26.3439 
26.3629 

8.8408 
8.8451 
8.8493 
8.8536 
8.8578 

696 
697 
698 
699 

700 

48  44  16 
48  58  09 
48  72  04 
48  86  oi 
49  oo  oo 

337  153  S36 
338  608  873 
340  068  392 
34i  532  099 
343  ooo  ooo 

26.3818 
26.4008 
26.4197 
26.4386 
26.4575 

8.8621 
8.8663 
8.8706 
8.8748 
8.8790 

47' 


DRAWING   AND    DESIGNING. 


Numbe 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

701 
702 

703 
704 

705 

49  14  01 

49  28  04 
49  42  09 
49  56  16 
•49  70  25 

344  472  101 
345  948  408 
347  428  927 
348  913  664 
350  402  625 

26.4764 
26.4953 
26.5141 
26.5330 
26.5518 

8.8833 
8.8875 
8.8917 
8.8959 
8.9001 

706 
707 
708 
709 
710 

49  84  36 
49  98  49 

50  12  64 

50  26  8  i 
50  41  oo 

351  895  816 

353  393  243 
354  894  912 
356  400  829 
357  911  ooo 

26.5707 
26.5895 
26.6083 
26.6271 
26.6458 

8.9043 
8.9085 
8.9127 
8.9169 
8.9211 

711 
712 

713 

7H 
715 

50  55  2C 
5°  69  44 
5083  69 
50  97  96 
51  J2  25 

359  425  43i 
360  944  128 
362  467  097 
363  994  344 
365  525  875 

26.6646 
266833 
26.7021 
26.7208 
26.7395 

8.9253 
8.9295 

89337 
8.9378 
8.9420 

7l6 
717 
7l8 
719 
720 

51  26  56 
51  40  89 

51  I5  24 
51  69  6  i 

51  84  oo 

367  06  i  696 
368  601  813 
370  146  232 
371  694  959 
373  248  ooo 

26.7582 
26.7769 
26.7955 
26.8142 
26.8328 

8.9462 
8.9503 

8-9545 
8.9587 
8.9628 

721 
722 

723 
724 

725 

51  98  41 

52  12  84 
52  27  29 
52  41  76 

S2  56  25 

374  805  361 
376  367  048 
377  933  067 

379  5°3  424 
381  078  125 

26.85.4 
26.8701 
26.8887 
26.9072 
26.9258 

8.9670 
8.9711 
8.9752 
8.9794 
89835 

726 
727 
728 
729 
73° 

52  70  76 
52  85  29 
52  99  84 
53  14  4i 
53  29  oo 

382  657  176 
384  240  583 
385  828  352 
387  420  489 
389  017  ooo 

26.9444 
26.9629 

26.98  1  5 
27.0000 
27.018:; 

8.9876 
8.9918 
8.9959 
9.OOOO 
9.0041 

731 
732 

733 
734 
735 

53  43  61 
53  58  24 
53  72  89 
53  87  56 
54  02  25 

390  617  891 
392  223  i  68 
393  832  837 
395  446  904 
397  065  375 

27.0370 
27-0555 
27.0740 
27.0924 
27.1109 

9.0082 
9.0123 
9.0164 
9.0205 
9.0246 

736 
737 
738 
739 
740 

54  16  96 
54  31  69 
54  46  44 
54  61  21 
54  76  oo 

398  688  256 
400  315  553 
401  947  272 

403  583  4'9 

405  224  ooo 

27.1293 
27.1477 
27.1662 
27.1846 
27.2029 

9.0287 
9.0328 
9.0369 
9.0410 
9.0450 

74i 
742 

743 
744 
745 

54  9°  81 
55  °5  64 
55  2°  49 
55  35  36 
55  5°  25 

406  869  02  1 
408  518  488 
410  172  407 
411  830  784 

413  493  625 

27.2213 
27.2397 
27.2580 
27.2764 
27.2947 

9.0491 

9.0532 
9.0572 

9  0613 
9.0654 

746 
747 
748 

749 

750 

55  65  16 
55  80  09 
55  95  04 
56  10  01 
56  25  oo 

415  i  60  936 
416  832  723 
418  508  992 
420  189  749 
421  875  ooo 

27.3130 

27-3313 
27.3496 
27.3679 
27.3861 

9.0694 

9.0735 
9.0775 
9.0816 
9.08  s6 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  4/ 


-16 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

75l 
752 
753 
754 

755 

56  40  oi 

56  55  04 
56  70  09 
56  85  16 
57  oo  25 

423  564  751 
425  259  008 

426  957  777 
428  66  i  064 
430  368  875 

27.4044 
27.4226 
27.4408 
27.4591 
27-4773 

9.0896 

9-0937 
9.0977 
9.IOI7 
9.1057 

756 
757 
75* 
759 
760 

57  15  3" 
57  3°  49 
57  45  64 
57  60  81 
57  76  oo 

432  081  216 
433  798  093 

435  5'9  5*2 

437  245  479 
438  976  ooo 

27-4955 
27.5136 

27-  S31  8 
27.5500 
27.5681 

9.1098 
9.1138 
9.1178 
9.1218 
9.1258 

76i 
762 
763 
764 
765 

57  9l  21 
5*  06  44 

58  21  69   . 
58  36  96 
58  52  25 

440  711  08  i 
442  450  728 
444  194  947 
445  943  744 
447  697  125 

27.5862 
27.6043 
27.6225 
27.6405 
27.6586 

9.1298 
9.1338 
9.1378 
9.1418 
9.1458 

766 
767 
768 
769 

770 

58  67  56 
58  82  89 
58  98  24 

59  13  61 
59  29  0° 

449  455  096 
451  217  663 
452  984  832 
454  756  6°9 
456  533  ooo 

27.6767 
27.6948 
27.7128 
27.7308 
27.7489 

9.1498 
9.1537 

9-1577 
9.1617 
9.1657 

771 
772 

773 
774 

775 

59  44  41 
59  59  84 
59  75  29 
59  9°  76 
60  06  25 

458  3H  on 
460  099  648 
461  889  917 
463  684  824 
465  484  375 

27.7669 
27.7849 
27.8029 
27.8209 

27.8388 

9.1696 
9.1736 

9-1775 
9.1815 
9.1855 

776 
777 
77* 
779 
780 

6O  21  76 

60  37  29 
60  52  84 
60  68  41 
60  84  oo 

467  288  576 
469  097  433 
470  910  952 
472  729  139 
474  552  ooo 

27.8568 
27.8747 
27.8927 
27.9106 
27.9285 

9.1894 
9-*933 
9.1973 
9.2012 
9.2052 

78i 
782 
783 
784 
785 

60  99  6  i 
61  15  24 
61  30  89 
6  1  46  56 
61  62  25 

476  379  54i 
478  2ii  768 
480  048  687 
481  890  304 
483  736  625 

27.9464 
27.9643 
27.9821 
28.0000 
28.0179 

9.2091 
9.2130 
9.2170 
9.2209 
9.2248 

786 

787 
788 
789 
790 

61  77  96 
61  93  69 
62  09  44 
62  25  21 
62  41  oo 

485  587  656 
487  443  403 
489  3°3  872 
491  169  069 
493  039  ooo 

28.0357 
28.0535 
28.0713 
28.0891 
28.1069 

9.2287 
9.2326 

9«  2365 

9.2404 

9.2443 

791 
792 

793 
794 
795 

62  56  81 
62  72  64 
62  88  49 
63  04  .36 

63  20  25 

494  913  67i 
496  793  088 
498  677  257 
500  566  184 
502  459  875 

28.1247 
28.1425 
28.1603 
28.1780 
28.1957 

9.2482 
9.2521 
9.2560 
9.2599 
9.2638 

796 

797 
798 

799 
800 

63  36  l6 
63  52  09 

63  68  04 
63  84  oi 
64  oo  oo 

504  358  336 
506  261  573 
508  169  592 
510  082  399 
512  ooo  ooo 

28.2135 
28.2312 
28.2489 
28.2666 
28.2843 

9.2677 
9.2716 
9.2754 
9.2793 
9.2832 

47] 


DRAWING   AND    DESIGNING. 


Numbei 

Square. 

Cube.           Square  Root. 

Cube  Root. 

80  I 
802 
803 
804 

805 

64  i  6  01 

64  32  04 
64  48  09 

64  64  16 

64  80  25 

513  922  401 
515  849  608 
517  781  627 
519  718  464 
521  660  125 

28.3019 
28.3196 
28.3373 
28.3549 
28.3725 

9.2870 
9.2909 
9.2948 
9.2986 

9-3025 

806 
807 
808 
809 

810 

64  96  36 
65  12  49 
65  28  64 
65  44  81 
65  61  co 

523  606  616 

525  557  943 
527  514  112 
529  475  129 

531  441  ooo 

28.3901 
28.4077 
28.4253 
28.4429 
28.4605 

9.3063 
9.3102 
9.3140 

9-3  '79 
9-32I7 

811 
812 
813 
8-14 
815 

65  77  21 

65  93  44 
66  09  69 
66  25  96 
66  42  25 

533  4n  731 
535  387  328 
537  367  797 
539  353  M4 
54i  343  375 

28.4781 
28.4956 
28.5132 
28.5307 
28.5482 

9-3294 
9-3332 
9-3370 
9.3408 

816 

817 
818 
819 
820 

66  5»  56 
66  74  89 
66  9  [  24 
67  07  61 
67  24  oo 

543  338  496 
545  338  5'3 
547  343  432 
549  353  259 
551  368  ooo 

28.5657 
28.5832 
28.6007 
28.6182 
28.6356 

9-3447 
9-3599 

821 
822 
823 
824 
825 

67  40  41 

67  56  84 
67  73  29 
67  89  76 
68  06  25 

553  387  66  i 
555  4i2  248 
557  44i  767 
559  476  224 
561  515  625 

286531 
28.6705 
28.6880 
28.7054 
28.7228 

9-3675 
93713 
9-3751 

826 
827 
828 
829 

830 

68  22  76 
68  39  29 
68  55  84 
68  72  41 
68  89  oo 

563  559  976 
565  609  283 
567  663  552 
569  722  789 
571  787  ooo 

28.7402 
28.7576 
28.7750 
28.7924 
28.8097 

9.3827 
9.3865 
9.3902 
9.3940 
9-3978 

831 
832 
833 
834 
835 

69  05  61 
69  22  24 
69  38  89 
69  55  56 
69  72  25 

573  856  191 

575  93°  368 
578  009  537 
580  093  704 
582  182  875 

28.8271 
28.8444 
28.8617 
28.8791 
28.8964 

9.4016 

9.4053 
9.4091 
9.4129 
9.4166 

oo  oo  oo  oo  oo 

4*.  co  Co  Co  Co 
O  MS  OO-vj  ON 

69  88  96 
70  05  69 
70  22  44 
70  39  21 
70  56  oo 

584  277  056 
586  376  253 
588  480  472 

59°  589  7i9 
592  704  ooo 

28.9137 
28.9310 
28.9482 
28.9655 
28.9828 

9.4204 
9.4241 

9.4279 
9.4316 

9-4354 

841 
842 

843 
844 
845 

70  72  8  i 
70  89  64 
71  06  49 
71  23  36 

71  40  25 

594  823  321 
596  947  688 
599  077  107 
601  211  584 

603  351  125 

29.0000 
29.0172 
29.0345 
29.0517 
29.0689 

9-4391 
9.4429 
9.4466 
9-4503 
9-4541 

846 
847 
848 

849 
850 

71  57  16 
71  74  09 
71  91  04 
•  72  08  01 
72  25  oo 

605  495  736 
607  645  423 
609  800  192 
611  960  049 
614  125  ooo 

29.0861 
29.1033 
29.  1  204 
29.1376 
29.1548 

9-4578 
9.4615, 
9.4652 
9.4690 
9.4727 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  47 ] 


Number 

Square. 

Cube. 

Square  Root, 

Cube  Root. 

85I 
8S2 
853 
854 
855 

72  42  oi 
72  59  04 
72  76  09 
72  93  16 
73  I0  25 

616  295  051 

618  470  208 
620  650  477 
622  835  864 
625  026  375 

29.1719 
29.1890 
29.2062 
29.2233 
29.2404 

9.4764 
9.4801 
9-4838 

9'4875 
9.4912 

856 

857 
858 
859 
860 

73  27  36 
73  44  49 
73  61  64 
73  78  81 
73  96  o° 

627  222  Ol6 

629  422  793 
631  628  712 

633  839  779 
636  056  ooo 

29-2575 
29.2746 
29.2916 
29.3087 
29.^,258 

9-4949 
9.4986 
9-5023 
9.5060 
9.5097 

86  1 
862 
863 
864 
865 

74  13  21 
74  3°  44 
74  47  69 
74  64  96 
74  82  25 

638  277  381 

640  503  928 
642  735  647 
644  972  544 
647  214  625 

29.3428 

29-3598 
29.3769 

29-3939 
29.4109 

9.5134 
9.5I7I 
9-5207 
9.5244 
9.5281 

866 
867 
868 
869 
870 

74  99  S6 
75  16  89 
75  34  24 
75  5i  61 
75  69  oo 

649  461  896 
651  7H  363 
653  972  032 
656  234  909 
658  503  ooo 

29.4279 

29-4449 
29.4618 
29.4788 
29.4958 

9-53<7 
9-5354 
9-5391 
9-5427 
9.5464 

871 
872 

873 

874 
875 

75  86  41 
76  03  84 
76  21  29 
76  38  76 

76  56  25 

660  776  311 
663  054  848 
665  338  617 

667  627  624 

669  921  875 

29.5127 
29.5296 
29.5466 

29-5635 
29.5804 

9.5501 
9-5537 
9-5574 
9.5610 

9-5647 

876 
877 
878 

879 
880 

76  73  76 
76  91  29 
77  08  84 
77  26  41 

77  44  oo 

672  221  376 
674  526  133 
676  836  152 

679  I51  439 
68  i  472  ooo 

29-5973 
29.6142 
29.6311 
29.6479   . 
29.6648 

9.5683 
9-57I9 
9-5756 
9-5792 
9.5828 

88  1 
882 
883 
884 
885 

77  or  61 
77  79  24 
77  96  89 
78  14  56 
78  32  25 

683  797  841 
686  128  968 
688  465  387 
690  807  104 
693  154  125 

29.6816 
29.6985 
29.7153 
29.7321 
29-7489 

9.5865 
9.5901 
9-5937 
9-5973 
9.6010 

886 
887 
888 
889 
890 

78  49  96 
78  67  69 
78  85  44 
79  03  21 
79  21  oo 

695  506  456 
697  864  103 
700  227  072 
702  595  369 
704  969  ooo 

29.7658 
29.7825 
29.7993 
29.8161 
29.8329 

9.6046 
9.6082 
9.6118 
9.6154 
9.6190 

891 
892 

893 
894 
895 

79  38  81 
79  56  64 
79  74  49 
79  92  36 
80  10  25 

707  347  97i 
709  732  288 
712  121  957 
714  516  984 
716  917  375 

29.8496 
29.8664 
29.8831 
29.8998 
29.9166 

9.6226 
9.6262 
9.6298 

9.6334 
9.6370 

896 
897 
898 
899 

900 

80  28  16 
80  46  09 
80  64  04 
80  82  oi 
8  i  oo  oo 

719  323  136 
721  734  273 
724  150  792 
726  572  699 
729  ooo  ooo 

29-9333 
29.9500 

29-9833 
3O.OOOO 

9.6406 
9.6442 
9.6477 
9-65I3 
9.6549 

47' 


DRA  WING   AND    DESIGNING. 


Numbe; 

Square. 

Cube.           Square  Root. 

Cube  Root. 

80  I 
802 
803 
804 
805 

64  i  6  oi 

64  32  04 
64  48  09 

64  64  16 

64  80  25 

513  922  4OI 
515  849  608 
517  781  627 
519  718  464 

521  660  125 

28.3019 
28.3196 

28.3373 
28.3549 
28.3725 

9.2870 
9.2909 
9.2948 
9.2986 
9-3025 

806 
807 
808 
809 

810 

64  96  36 
65  12  49 
65  28  64 
65  44  8[ 
65  61  co 

523  606  616 
525  557  943 
527  5'4  112 
529  475  129 
531  441  ooo 

28.3901 
28.4077 
28.4253 
28.4429 

28.4605 

9.3063 
9.3102 
9.3140 

9-3  '79 
9.3217 

811 
812 

8J3 
814 
815 

65  77  21 

65  93  44 
66  09  69 
66  25  96 
66  42  25 

533  411  731 
535  387  328 
537  367  797 
539  353  144 
54i  343  375 

28.4781 
28.4956 
28.5132 
28.5307 
28.5482 

9-3294 
9-3332 
9-3370 
9.3408 

816 
817 
818 
819 

820 

66  5»  56 
66  74  89 
66  91  24 
67  07  61 
67  24  oo 

543  338  496 
545  338  5T3 
547  343  432 
549  353  259 
551  368  ooo 

28.5657 

28.5832 
28.6007 
28.6182 
28.6356 

9-3447 
9-3599 

821 
822 
823 
824 
825 

67  40  41 
67  56  84 
67  73  29 
67  89  76 
68  06  25 

553  387  661 
555  412  248 
557  441  767 
559  476  224 
561  515  625 

286531 

28.6705 

28.6880 
28.7054 
28.7228 

9-3637 
9-3675 
93713 
9-3751 

oc  oo  oo  oo  oo 
OJ  to  to  to  to 
O  vO  OQ^-J  ON 

68  22  76 
68  39  29 
68  55  84 
68  72  41 
68  89  oo 

563  559  976 
565  609  283 
567  663  552 
569  722  789 
571  787  ooo 

28.7402 

28.7576 
28.7750 
28.7924 
28.8097 

9.3827 

9.3902 
9.3940 
9-3978 

831 
832 

833 
834 
835 

69  05  61 
69  22  24 
69  38  89 
69  55  56 
69  72  25 

573  856  191 
575  930  368 
578  009  537 
580  093  704 
582  182  875 

28.8271 

28.8444 
28.8617 
28.8791 
28.8964 

9.4016 

9-4053 
9.4091 
9.4129 
9.4166 

836 

837 
838 

839 
840 

69  88  96 
70  05  69 
70  22  44 
70  39  21 
70  56  oo 

584  277  056 
586  376  253 
588  480  472 
590  589  719 
592  704  ooo 

28.9137 
28.9310 
28.9482 
28.9655 
28.9828 

9.4204 
9.4241 

9.4279 
9.4316 

9-4354 

841 
842 
843 
844 
845 

70  72  81 
70  89  64 
71  06  49 
71  23  36 
71  40  25 

594  823  321 
596  947  688 
599  077  107 
601  211  584 
603  351  125 

29.0000 
29.0172 

29.0345 
29.0517 

29.0689 

9-4391 
9.4429 
9.4466 
9-4503 
9-4541 

846 
847 
848 

849 
850 

71  57  16 
71  74  09 
71  91  04 
•  72  08  oi 
72  25  oo 

605  495  736 
607  645  423 
609  800  192 
611  960  049 
614  125  ooo 

29.0861 

29.1033 

29.1204 

29.1376 
29.1548 

9-4578 
9.4615 
9.4652 
9.4690 
9.4727 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.  47 ] 


Number 

Square. 

Cube. 

Square  Root, 

Cube  Root. 

85I 
852 
853 
854 
855 

72  42  oi 
72  59  04 
72  76  09 
72  93  16 
73  10  25 

616  295  051 
618  470  208 
620  650  477 
622  835  864 
625  026  375 

29.1719 
29.1890 
29.2062 
29.2233 
29.2404 

9,4764 
9.4801 
9.4838 

9-4875 
9.4912 

856 

857 

858 

859 
860 

73  27  36 
73  44  49 
73  61  64 
73  78  81 
73  96  oo 

627  222  016 
629  422  793 
631  628  712 

633  839  779 
636  056  ooo 

29-2575 
29.2746 
29.2916 
29.3087 

29.  ;258 

9.4949 
9.4986 
9.5023 
9.5060 

9.5097 

86  1 
862 
863 
864 
865 

74  13  21 
74  3°  44 
74  47  69 
74  64  96 
74  82  25 

638  277  381 

640  503  928 
642  735  647 
644  972  544 
647  214  625 

29.3428 

29-3598 
29.3769 

29-3939 
29.4109 

9.5134 
9.5I7I 
9.5207 
9.5244 
9.5281 

866 
867 
868 
869 
870 

74  99  56 
75  16  89 
75  34  24 
75  5i  61 
75  69  oo 

649  461  896 
651  7H  363 
653  972  032 
656  234  909 
658  503  ooo 

29.4279 
29.4449 
29.4618 
29.4788 
29.4958 

9-53»7 
9-5354 
9-5391 
9-5427 
9.5464 

871 

872 
873 
874 
875 

75  86  41 
76  03  84 

76  21  29 
76  38  76 
76  56  25 

660  776  311 

663  054  848 
665  338  617 

667  627  624 
669  921  875 

29.5127 
29.5296 
29.5466 

29-5635 
29.5804 

9.5501 
9-5537 
9-5574 
9.5610 
9.5647 

876 

877 
878 

879 
880 

76  73  76 
76  91  29 
77  08  84 
77  26  41 

77  44  oo 

672  221  376 
674  526  133 
676  836  152 

679  *Sl  439 
68  i  472  ooo 

29-5973 
29.6142 
29.6311 
39.6479  . 
29.6648 

9.5683 
9-57I9 
9-5756 
9-5792 
9.5828 

88  1 
882 
883 
884 
885 

77  61  61 

77  79  24 
77  96  89 
78  14  56 
78  32  25 

683  797  841 
686  128  968 
688  465  387 
690  807  104 
693  154  125 

29.6816 
29.6985 
29.7153 
29.7321 
29.7489 

9.5865 
9.5901 
9-5937 
9-5973 
9.6010 

886 
887 
888 
889 
890 

78  49  96 
78  67  69 
78  85  44 
79  03  21 
79  21  oo 

695  506  456 
697  864  103 
700  227  072 
702  595  369 
704  969  ooo 

29.7658 
29.7825 
29.7993 
29.8161 
29.8329 

9.6046 
9.6082 
9.6118 
0,6154 
9.6190 

891 
892 

893 
894 
895 

79  38  81 
79  56  64 
79  74  49 
79  92  36 
80  10  25 

707  347  97i 
709  732  288 
712  121  957 
714  516  984 
716  917  375 

29.8496 
29.8664 
29.8831 
29.8998 
29.9166 

9.6226 
9.6262 
9.6298 
9-6334 
9-6370 

896 

897 
898 
899 

900 

80  28  16 
80  46  09 
80  64  04 
80  82  oi 
810000 

719  323  136 
721  734  273 
724  150  792 
726  572  699 
729  ooo  ooo 

29-9333 
29,9500 
29.9666 

29-9833 
30.0000 

9.6406 
9.6442 
9.6477 
9-65!3 
9-6549 

47 


19 


DRAWING   AND   DESIGNING. 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

9OI 

902 

9°3 
904 

905 

81  18  01 
81  36  04 
81  54  09 
81  72  16 
81  90  25 

731  432  701 

733  870  808 

736  3H  327 
738  763  264 
741  217  625 

30.0167 

30.0333 
30.0500 
30.0666 
30.0832 

9.6585 
9.6620 
9.6656 
9.6692 
9.6727 

906 
907 
908 
909 
910 

82  08  36 
82  26  49 
82  44  64 
82  62  81 
82  81  oo 

743  677  4i6 
746  142  643 
748  613  312 
751  089  429 

753  571  ooo 

30.0998 
30.1164 

30.1330 
30.1496 
30.1662 

9.6763 
9.6799 
9.6834 
9.6870 
9.6905 

911 
912 

9i3 
914 

9'5 

82  99  21 

83  17  44 
83  35  69 
83  53  96 

83  72  25 

756  058  031 
758  550  825 
761  048  497 

763  551  944 

766  060  875 

30.1828 

30.1993 
30.2159 
30.2324 
30.2490 

9.6941 
9.6976 
9.7012 

9-7047. 
9.7082 

916 
917 
918 
919 
920 

83  90  56 
84  08  89 
84  27  24 
84  45  61 
84  64  oo 

768  575  296 
771  095  213 
773  620  632 

776  151  559 

778  688  ooo 

30.2655 
30.2820 
30.2985 
30.3150 
30.3315 

9.7118 

9'7I53 
9.7188 
9.7224 
9-7259 

921 
922 

923 
924 

925 

84  82  41 
85  oo  84 
85  19  29 
85  37  76 
85  56  25 

781  229  901 

783  777  448 
786  330  467 
788  889  024 
79i  453  !25 

30.3480 

30.3645 
30.3809 

30.3974 
30,4138 

9-7294 
9.7329 
9-7364 
9.7400 

9-7435 

926 
927 
928 
929 

930 

85  74  76 
85  93  29 
86  ii  84 
86  30  41 
86  49  oo 

794  022  776 
796  597  983 

799  178  752 
801  765  089 
804  357  ooo 

30.4302 
30.4467 
30.4631 
30.4795 
30.4959 

9.7470 

9-7505 
9-7540 

9-7575 
9.7610 

931 
932 
933 
934 

935 

86  67  61 
86  86  24 
87  04  89 
87  23  56 
87  42  25 

806  954  491 
809  557  568 
812  166  237 
814  780  504 
817  400  375 

30.5123 
30.5287 

30.5450 
30.5614 

30.5778 

9-7645 
9.7680 

9-77I5 
9-7750 
9-7785 

936 
937 
938 

939 

940 

87  60  96 

87  79  69 
87  98  44 
88  17  21 
88  36  oo 

820  025  856 
822  656  953 
825  293  672 
827  936  019 
830  584  ooo 

30-594I 
30.6105 
30.6268 
30.6431 
30.6594 

9.7819 

9-7854 
9.7889 
9.7924 
9-7959 

941 
942 
943 
944 

945 

88  54  81 
88  73  64 
88  92  49 
89  ii  36 
89  30  25 

833  237  621 

835  896  888 
838  561  807 
841  232  384 
843  908  625 

30-6757 
30.6920 
30.7083 
30.7246 
30.7409 

9-7993 
9.8028 
9.8063 
9.8097 
9.8132 

946 

947 
948 

949 
950 

89  49  16 
89  68  09 
89  87  04 
90  06  01 
90  25  oo 

846  590  536 
849  278  123 

851  97i  392 
854  670  349 

857  375  °°o 

30.7571 
30-7734 
30.7896 
30.8058 
30.8221 

9.8167 
9.8201 
9.8236 
9.8270 

9.8305 

USEFUL   TABLES  AND  MISCELLANEOUS  INFORMATION.   4f 


Number 

Square. 

Cube. 

Square  Root. 

Cube  Root. 

951 

952 

953 
954 
955 

90  44  01 
90  63  04 
90  82  09 
91  01  16 
91  20  25 

860  085  351 

862  80  I  408 
865  523  177 

868  250  664 
870  983  875 

30.8383 

30.8545 
30.8707 
30.8869 
30.9031 

9.8339 
9-8374 
9.8408 
9.8443 
9.8477 

956 

957 
958 

959 

91  39  36 
91  58  49 
91  77  64 
91  96  8  i 
92  16  oo 

873  722  816 
876  467  493 
879  217  912 
88  i  974  079 
884  736  ooo 

30.9192 

30.9354 
30.9516 
30.9677 
30.9839 

9.8511 
9.8546 
9.8580 
9.8614 
9.8648 

gi 

962 

963 
964 
965 

92  3  21 
92  54  44 
92  73  69 
92  92  96 
93  12  25 

887  503  68  i 
890  277  128 
893  056  347 
895  841  344 
898  632  125 

31.0000 
3I.Ol6l 
31.0322 
31.0483 
31.0644 

9.8683 
9.8717 
9.8751 
9.8785 
9.8819 

966 
967 
968 
969 
970 

93  3i  f 
93  50  89 
93  70  24 
93  89  61 
94  09  oo 

901  428  696 
904  231  063 
9°7  039  232 
909  853  209 
912  673  ooo 

31.0805 
31.0966 
31.1127 
31.1288 
31.1448 

9.8854 
9.8888 
9.8922 
9.8956 
9.8990 

971 
972 
973 
974 

975 

94  28  41 
94  47  84 
94  67  29 
94  86  76 
95  06  25 

915  498  6u 
918  330  048 
921  167  317 
924  oio  424 
926  859  375 

31.1609 
31.1769 
3I.I929 
31.2090 
31.2250 

9.9024 
9.9058 
9.9092 
9.9126 
9.9160 

976 

977 
978 

979 

980 

95  25  76 

95  45  29 
95  64  84 

95  84  41 
96  04  oo 

929  714  176 
932  574  833 
935  44i  352 
938  3i3  739 
941  192  ooo 

31.2410 
31.2570 
31.2730 
31.2890 
31.3050 

9.9194 
9.9227 
9.9261 
9.9295 
9.9329 

981 
982 

983 
984 
985 

96  23  61 
96  43  24 
96  62  89 
96  82  56 
97  02  25 

944  076  141 
946  966  i  68 
949  862  087 
952  763  904 
9-5  671  625 

31.3209 

3I-3369 
3L3528 
3I.3688 
3I-3847 

9.9363 
9'9396 
9-9430 
9.9464 

9-9497 

986 
987 
988 
989 
990 

97  21  96 
97  41  69 
97  61  44 
97  81  21 
98  01  oo 

958  585  256 
961  504  803 
964  430  272 
967  361  669 
970  299  ooo 

31.4006 
31.4166 

3L4325 
31.4484 

3L4643 

9-9531 
9-9565 
9.9598 
9.9632 
9.9666 

991 
992 
993 
994 
995 

98  20  81 

«  98  40  64 
98  60  49 
98  80  36 
99  oo  25 

973  242  271 
976  191  488 
979  146  657 
982  107  784 
985  074  875 

31.4802 
31.4960 

3I.5"9 
3L5278 
3L5436 

99699 
9-9733 
9.9766 
9.9800 
9-9833 

996 

997 
998 

999 

TOGO 

99  20  16 
99  40  09 
99  60  04 
99  80  01 

I  OO  OO  OO 

988  047  936 
991  026  973 
994  on  992 
997  002  999 

I  OCO  OOO  OOO 

3L5595 
3L5753 
3I.59H 
31.6070 
31.6228 

9.9866 
9.9900 
9-9933 
9.9967 

IO.OOOO 

CHAPTER  I.* 
SCREWS,  NUTS,  AND  BOLTS. 

A  Screw  is  a  helical  projection  or  thread  formed  upon  a 
cylinder  and  is  the  most  common  device  used  in  mechanical 


FIG.  28. 

combinations.      It  is  employed   in  the  construction    of  ma- 
chinery   for    producing    pressure    contact    and    transmitting 

*  Copyright. 


SCREWS,  NUTS,  AND    BOLTS.  49 

motion.  When  the  thread  of  an  external  screw  is  made  to 
fit  into  the  corresponding  hollow  of  an  internal  screw 
(Fig.  28)  the  latter  is  termed  its  nut. 

The  Pitch  of  a  Screw-thread  is  the  lineal  distance  its 
nut  would  advance  along  the  axis  in  one  turn.  In  a  single- 
threaded  screw  the  pitch  is  the  distance  between  the  centres 
of  two  consecutive  threads  measured  in  the  direction  of  the 
axis,  in  a  double-threaded  screw  it  is  the  distance  from 
centre  to  centre  of  every  alternate  thread,  and  in  a  triple- 
threaded  screw  it  is  a  distance  that  will  embrace  three  threads. 
For  screw-fastenings,  instead  of  giving  the  pitch  the  number 
of  threads  per  inch  of  screw  is  given — for  example,  a  bolt 
of  i"  diameter  has  generally  8  threads  per  inch;  this  means 
that  the  bolt  has  a  single  thread  wound  around  it  8  times  for 
every  inch  of  its  length. 

Right-  and  Left-handed  Screws. — Screws  are  made 
right-  and  left-handed,  of  which  the  right-handed  are  the 
more  common  and  are  distinguished  by  their  nuts  advancing 
along  the  screws  when  turned  in  the  direction  in  which  the 
hands  of  a  watch  revolve.  On  a  drawing  the  right-handed 
screws  are  distinguished  by  the  threads  inclining  upwards 
towards  the  right  hand  when  the  screws  are  in  a  vertical 
position,  as  in  Fig.  28.  When  a  nut  with  a  right-handed 
thread  is  shown  in  section  the  direction  of  the  threads  in  the 
nut  is  the  opposite  to  the  threads  on  the  screw. 

The  Nominal  Diameter  of  a  Screw  is  the  diameter  over 
the  tops  of  the  threads  and  is  equal  to  the  diameter  of  the 
cylinder  upon  which  the  thread  is  cut.  It  is  the  area  of  the 
nominal  diameter  that  is  considered  when  estimating  the 
shearing;  strength. 


U    UNIVLR5ITY    M 
SO  DRA  WING  AND  DESIGNING. 

The  Effective  Diameter  is  the  diameter  at  the  bottom 
of  the  thread  and  is  equal  to  the  diameter  of  the  hole  in  the 
nut  before  its  threads  are  cut.  Unless  when  the  bolts  are 
subjected  to  a  shearing  stress,  it  is  the  area  of  the  effective 
diameter  that  is  considered  in  estimating  their  strength. 

The  Depth  of  the  Thread  is  the  distance  measured 
perpendicularly  to  the  axis  of  the  screw  from  the  top  to  the 
bottom  of  the  thread. 

NOTATION. 

d =  nominal  diameter  of  bolt; 

d^=  effective  diameter  of  bolt; 

d  =  depth  of  thread  ; 

<?,=  total  depth  of  V; 

/  =  pitch  of  thread ; 

n  =  number  of  threads  per  inch. 

The  Forms  of  Screw-threads  in  general  use  in  machine 
construction  are  represented  in  Figs.  29—33.  The  V  thread 
is  adopted  on  all  screw-fastenings  because  of  the  shearing 
strength  of  the  threads  and  frictional  holding  power,  which 
is  due  to  the  normal  pressure  on  the  thread  being  inclined 

r  V 


FIG.  29 

to  the  axis  of  the  screw.     This  normal   force   N,   Fig.   29, 
may  be  resolved  into  two  components,  one  L  parallel  to  the 


SCREWS,  NUTS,  AND   BOLTS.  $1 

axis  of  the  screw,  and  the  other  R  at  right  angles  to  it. 
L  represents  the  load  carried  by  the  thread  and  R  the  force 
tending  to  burst  the  nut ;  therefore  the  greater  the  angle 
of  the  V  the  greater  will  be  the  normal  component  or 
bursting  force,  and,  the  friction  being  proportional  to  the 
normal  force,  it  will  increase  with  the  angle  of  the  V.  Of 
the  forms  of  V  threads  shown  two  (Figs.  29  and  33)  are  in 
common  use  in  the  United  States  for  bolts  and  nuts. 

The  Sellers  or  United  States  Standard,  a  section  of 
which  is  shown  in  Fig.  29,  has  been  adopted  by  the  U.  S. 
Government,  the  Railway  Master  Mechanics'  Association,  the 
Master  Car-builders'  Association,  and  many  of  the  principal 
manufactories  in  this  country.  The  sides  of  this  thread 
form  an  angle  of  60°  with  each  other,  and  are  \  of  tf,  short  of 
meeting  at  a  sharp  point  at  the  tops  and  bottoms,  which 
makes  the  sides  of  the  thread  in  length  equal  to  J  of  the 
pitch,  and  the  depth  of  thread  8  will  be  expressed  by  the 
formula 

d  =  }  X  /  sin  60°  =  o.65/ (i) 

The  effective  diameter  will  then  be 

dl  =  d-2d  =  d-i.$p  =  d-  ^.     ...'-.     (2) 

n 

The  relation  between  the  pitch  and  the  diameter  will  be  ex- 
pressed by  the  formula 


p  =  0.24  y^_f_  0!625  _  0.175.       •      •      •     (3) 
The  number  of  threads  per  inch  is 


0.24^+0.625  -0.175 


"      "     ™ 


52  DRAWING  AND   DESIGNING. 

The  table  of  proportions  on  page  70  has  been  deduced  from 
the  preceding  formulae.  A  difference,  however,  may  be  found 
between  the  formulae  and  the  table  in  the  number  of  threads 
per  inch,  as  the  table  has  been  modified  to  avoid  as  far  as 
practicable  troublesome  combinations  in  the  gears  of  screw- 
cutting  machines. 

Exercise  i. — Draw  6  threads  in  sectional  outline,  of  the 
Sellers  thread  (Fig.  29),  suitable  for  a  screw  6"  in  diameter. 
Scale  three  times  full  size. 

Construction. — Begin  by  drawing  a  horizontal  line  in  the 
upper  left-hand  corner  of  the  paper  f "  down  from  the  border- 
line, and  a  vertical  line  about  £ "  in  from  the  left-hand  border- 
line. Then  find  the  pitch  /  by  the  formula  (3),  and  from 
where  the  two  lines  you  have  just  drawn  intersect  mark  off 
with  the  scale  on  the  horizontal  line  6  points  a  distance 
apart  equal  to  the  pitch  as  found  by  the  formula.  Through 
these  points  with  the  30°  triangle  draw  the  Vs.  Complete 
the  pencilling  by  dividing  the  depth  of  the  V  into  8  equal 
divisions,  and  cut  off  one  division  at  the  top  and  bottom  of 
each  thread. 

The  Sharp  V  Thread,  shown  in  Fig.  30,  is  one  of  the 


i.. 


FIG.  30. 
forms  of  threads  that  were  in  use  before  the  Sellers  thread 


SCREWS,  NUTS,  AND   BOLTS.  53 

\vas  adopted  as  the  U.  S.  standard,  and  is  still  used,  although 
condemned  by  all  progressive  engineers.  This  thread  is  the 
same  as  the  Sellers  thread  except  that  the  sides  are  made  to 
meet  at  a  sharp  point  at  the  top  and  bottom,  which  makes 
the  sides  of  the  thread  equal  in  length  to  the  pitch/,  and 
the  depth  of  the  thread  #,  will  be  expressed  by  the  formula 

^  =/  sin  60°  =  0.866/ A     (5) 

The  effective  diameter  of  the  bolt  (</,)  will  then  be  expressed 
by  the  formula 

d,  =  d—  2  X  o.866/=  d—  1.732.        ;     .     (6) 
Now,  comparing  the  effective  diameters,  we  have : 

U.  S.  threads  d,  =  d  —  i.$p.     .     .    '-'-..    ".     .     .     (2) 

V threads  d,  =  d—  i.7$2p.       .     .   - «     .     ,      (6) 

This  serves  to  show  that  with  an  equal  pitch  the  effective 
diameter  of  the  screw  having  a  U.  S.  standard  thread  is 
greater  than  one  with  a  sharp  V  thread.  While  the  latter  form 
of  thread  materially  diminishes  the  strength  of  the  bolt,  the 
sharp  point  adds  very  little  strength  to  the  thread,  A  fur- 
ther objection  to  this  form  of  thread  is  the  variation  in  depth 
of  the  threads  due  to  the  wear  of  the  sharp  points  on  the  taps 
and  dies  used  in  producing  them. 

The  Whitworth  V  Thread,  an  outline  section  of  which 
is  shown  in  Fig.  31,  is  the  British  standard,  and  is  generally 
adopted  on  all  screw-fastenings  in  British  machine  construc- 
tion. It  has  the  sides  of  the  V  inclined  to  each  other  at  an 
angle  of  55°,  and  has  an  amount  rounded  off  at  the  top  and 
bottom  equal  to  \  of  the  total  depth  of  the  V.  The  table  of 


54 


DRAWING   AND    DESIGNING. 


dimensions  for  Wkitworth  screws  (page  70)  has  been  deduced 
from  the  following  formulae.      The  total  depth  of  the  V 

di==  0.5  cot  27!°  =  o.96/ (7) 


FIG.  31. 
The  depth  of  the  finished  thread 

d  =  |  X  o.96/=  0.64^.       .     .     .     .     (8) 

The  pitch  /  =  0.08^  +  0.04 (9) 

Number  of  threads  per  inch 


i  i 

=  —     and     p  =  — 

p  *       n 


(10) 


The  diameter  at  the  bottom  of  the  thread  will  be  given  by 

the  formula 

1.28 
dl  =  d—  2  X  0.64/  =  d ..     .     .     (n) 

Exercise  2. — Draw  6  threads  of  the  Whitworth  form  of 
thread  (Fig.  31).  Pitch  i".  Scale  three  times  full  size. 

Construction. — At  a  suitable  distance  below  the  drawing 
of  the  Sellers  thread  draw  two  horizontal  lines  parallel  to 
each  other  and  a  distance  apart  equal  to  O.g6p.  On  the 
upper  line  mark  off  a  distance  ab  equal  to  the  pitch.  Bisect 


SCKEWS,  NUTS,  AND   BOLTS.  55 

ab  and  draw  the  bisecting  line  to  cut  the  lower  parallel  line 
at  the  point  c.  Join  ca  and  cb,  which  will  be  inclined  to  each 
other  at  an  angle  of  55°:  Mark  off  the  pitch  from  b  along 
the  upper  line,  and  from  c  along  the  lower  line,  to  give  the 
required  number  of  threads.  Complete  the  pencilling  by 
rounding  off  the  sharp  points  of  the  V. 

The  Square  Screw-thread. — The  form  of  thread  which 
is  invariably  called  the  square  thread  is  really  a  rectangle, 
the  depth  of  the  thread  being  equal  to  o.^^p  and  its  width 
equal  to  o.  5/.  However,  it  is  usual  and  accurate  enough 
to  make  it  square  upon  the  drawing.  On  screws  of  the 
same  diameter  the  pitch  of  a  square-threaded  screw  is  usually 
made  equal  to  twice  the  pitch  of  one  with  a  V  thread ; 
therefore  the  square  thread  will  have  only  half  the  amount 
of  material  at  the  bottom  of  the  thread  that  the  V  thread 
has  to  resist  the  shearing  action  of  the  load.  As  the  bearing- 
surfaces  of  this  screw  are  perpendicular  to  the  axis,  and  the 
force  applied  parallel  to  it,  there  will  be  no  bursting  force 
upon  the  nut ;  and  as  the  reaction  is  nearly  equal  to  the  load 
on  the  square-threaded  screw,  there  will  be  less  friction  than 
there  is  under  the  same  conditions  with  a  V  thread;  conse- 
quently the  square  thread  is  best  adapted  for  transmitting 
motion  when  the  load  has  to  be  moved  in  opposite  directions. 

The  Knuckle  or  Rounded  Screw-thread  is  a  modifica- 
tion of  the  square  thread  in  which  the  top  and  bottom  of  each 
thread  are  made  semicircular,  as  shown  in  Fig.  32.  This  form 
of  thread  is  used  for  rough  work  and  can  be  readily  thrown 
in  and  out  of  gear  with  a  portion  of  a  nut. 

The  Buttress  Screw-thread  is  a  combination  of  the  V 
and  square  threads,  one  side  being  perpendicular,  and  the 


DRAWING   AND   DESIGNING. 


other  inclined   at   an  angle  of  45°  to  the  axis  of  the  screw, 
and    has  an  amount   cut    from  the  top  and  bottom  of  each 


J 


FIG.  32. 

thread  equal  to  -J  of  the  total  depth  of  the  thread,  as  shown 
in  Fig.  33.  This  form  of  thread  can  be  used  only  when  the 
pressure  is  on  that  side  of  the  thread  which  is  at  right  angles 
to  the  axis  of  the  screw. 


FIG.  33. 

Exercise  3. — Draw  the  sectional  outline  of  the  square, 
knuckle,  and  buttress  threads  shown  in  Figs.  32  and  33. 
Pitch  i" '.  Scale  twice  full  size. 

Pipe-threads — Previous  to  the  year  1862  no  common 
system  had  been  agreed  upon  for  the  form  or  proportions 
of  pipe-threads.  Since  that  time,  owing  to  the  efforts  of 
the  late  Robert  Briggs,  C.E.,  who  proposed  formulae  and 
tables  for  the  dimensions  of  pipes  and  pipe-threads,  a  standard 


SCXEWS,  NUTS,  AND   BOLTS. 


57 


TABLE   1. 

STANDARD  DIMENSIONS  OF  WROUGHT-IRON  WELDED  TUBES. 
(BRIGGS  STANDARD.) 


Diameter  of  Tube. 

Thickness 
of 
Metal. 

Screwed  Ends. 

Nominal 
Inside. 

Actual 
Inside. 

Actual 
Outside. 

Number  of 
Threads  per 
Inch. 

Length  of 
Perfect 
Screw. 

Inches. 

Inches. 

Inches. 

Inch. 

No. 

Inches. 

\ 

0.270 

0.405 

0.068 

27 

O.ig 

I 

0.364 

0.540 

0.088 

18 

0.29 

1 

0.494 

0.675 

0.091 

18 

0.30. 

i 

0.623 

0.840 

0.109 

14 

0-39 

1 

0.824 

1.050 

O.II3 

14 

0.40 

I 

1.048 

I.3I5 

0.134 

Hi 

0.51 

I* 

1.380 

1.660 

0.140 

ii 

0.54 

Ii 

1.610 

I.gOO 

0.145 

"i 

0-55 

2 

2.067 

2.375 

0.154 

"i 

0.58 

2i 

2.468 

2.875 

0.204 

8 

0.89 

3 

3-067 

3-500 

O.2I7 

8 

0-95 

3i 

3-548 

4.000 

0.226 

8 

.00 

JL 

4.026 

4-500 

0.237 

J 

•05 

4i 

4-508 

5.000 

<572~46 

8 

.fo 

5 

5-045 

5.563 

0.259 

8 

.16 

6 

6.065 

6.625 

0.280 

8 

.26 

7 

7-023 

7-625 

0.301 

8 

.36 

8 

7.982 

8.625 

0.322 

8 

.46 

9 

.9.000 

9-625 

0.344 

8 

•57 

10 

10.019 

10.750 

0.366 

8 

.68 

•     Taper  of  conical  tube-ends,  i  in  32  to  axis  of  tube  (f  in.  per  foot  total  taper). 

system  has  been  generally  used  and  was  formally  adopted  by 
the  manufacturers  of  wrought-iron  pipes  and  boiler-tubes  and 
v-  by  the  Association  of  Manufacturers  of  Brass  and  Iron  Steam-, 
Gas-,  and  Water-work  of  the  United  States. 

The  following  is  an  extract  from  a  paper  by  Mr.  Briggs 
as  given  in  the  report  of  the  American  Society  of  Engineers: 

"  The  thread  employed  has  an  angle  of  60°;  it  is  slightly 
rounded  off,  both  at  the  top  and  at  the  bottom,  so  that  the 
height  or  depth  of  the  thread,  instead  of  being  exactly  equal 
to  the  pitch,  is  only  four  fifths  of  the  pitch,  or  equal  to  o.8i, 


So  DRAWING   AND   DESIGNING. 

if  n  be  the  number  of  threads  per  inch.  For  the  length 
of  tube-end  throughout  which  the  screw-thread  continues 
perfect  the  empirical  formula  used  is  T=  (p.8D  -J-  4.8)  X  — , 
where  D  is  the  actual  external  diameter  of  the  tube  through- 
out its  parallel  length,  and  is  expressed  in  inches.  Further 
back,  beyond  the  perfect  threads,  come  two  having  the  same 
taper  at  the  bottom,  but  imperfect  at  the  top.  The  remain- 
ing imperfect  portion  of  the  screw-thread,  furthest  back  from 
the  extremity  of  the  tube,  is  not  essential  in  any  way  to  this 
system  of  joint ;  and  its  imperfection  is  simply  incidental  to 
the  process  of  cutting  the  thread  at  a  single  operation. 

Exercise  4. — Draw  a  section  of  a  pipe-screw  (Fig.  34)  for 
a  wrought-iron  pipe  8"  in  diameter.      Scale  five  times  full  size. 


T w 


FIG.  34. 

Construction. — Draw  two  lines  parallel  to  each  other  at 
a  distance  apart  equal  to  the  thickness  of  metal  as  given  in 
the  table;  then  draw  the  vertical  line  2  to  represent  the  end 
of  the  pipe,  and  from  2  along  the  line  I  mark  off  3,  4,  equal 
to  T.  Taper  I  in  32  means  an  inclination  of  I  unit  in  height 
to  every  32  units  in  length.  From  the  point  4  draw  the  line  5 
at  the  required  inclination.  On  the  line  5  from  where  it 
intersects  2  mark  off  points  at  a  distance  apart  equal  to  the 
pitch,  and  through  these  points  with  the  30°  triangle  draw  the 


SCKEWS,  NUTS,    AND   BOLTS. 


59 


threads.  The  bottoms  of  the  last  4  threads  are  cut  off  by 
drawing  a  line  from  the  bottom  of  the  last  thread  that  is 
full  at  the  bottom  to  a  point  on  the  surface  of  the  pipe  which 
is  a  distance  beyond  the  screwed  part  equal  to  the  pitch. 

Screw-thread  Conventions. — The  method  of  drawing 
screws  to  represent  their  tnre  form  is  shown  in  Fig.  28, 
but  it  is  quite  obvious  that  it  is  unnecessary  for  the  drafts- 
man to  perform  this  lengthy  geometrical  construction  to 
indicate  each  screwed  piece  upon  the  drawing.  Instead 
he  adopts  some  convention  suitable  to  the  class  of  drawr 
ing  he  is  making  that  can  be  quickly  drawn  and  is  generally 
understood  to  represent  a  screw-thread.  Fig.  35,  No.  I, 


FIG.  35. 

shows  a  convention  for  a  double  V  thread;  No.  2,  a  single 
V  thread;  No.  3,  a  single  square  thread;  No.  4,  a  single 
left-hand  V  thread;  No.  5,  a  double  right-hand  square 
thread;  No.  6,  any  V  thread  of  small  diameter;  No.  7, 
any  thread  of  very  small  diameter.  The  method  adopted 
oa  rough  drawings  and  sketches  is  shown  at  No.  7.  The 
dotted  lines  indicate  the  bottom  of  the  thread,  and  the 
distance  they  extend  along  the  piece  the  length  of  the 


6O  DRAWING   AND   DESIGNING. 

screwed  part.  At  Nos.  I,  2,  4  are  shown  conventions 
adopted  upon  finished  drawings  to  represent  threaded  screws 
of  a  large  diameter 'and  wide  pitch.  There  are  various  ways 
of  improving  the  appearance  of  this  convention :  one  is 
by  shading  the  lower  lines  of  each  thread,  as  shown  in  Fig. 
37,  and  another  method  is  to  fill  in  completely  the  under 
side  of  the  thread,  as  shown  in  Fig.  39.  At  No.  6  is 
shown  a  method  adopted  on  working  drawings  to  represent 
screw-threads  upon  pieces  of  a  small  diameter  or  large  screws 
drawn  to  a  small  scale.  Here  the  narrow  lines  indicate  the 
top  and  the  wide  lines  the  bottom  of  the  screw-thread. 
When  a  very  long  screw  has  to  be  represented  upon  a  draw- 
ing, as  is  often  the  case  with  the  square-threaded  screw,  a 
few  threads  are  drawn  at  the  beginning  of  the  screwed  part, 
and  the  length  of  the  screw  is  indicated  by  dotted  lines  drawn 
from  the  bottoms  of  the  threads. 

The  Nut. — The  most  common  application  of  the  screw 
for  producing  contact  pressure  is  the  bolt,  used  in  conjunction 
with  a  nut,  of  which  there  are  different  forms.  The  form, 
most  in  use  is  the  hexagonal  (Fig.  37). 

The  standard  proportions  for  hexagonal  nuts  are : 

H  •=•  height  =  diameter  of  bolt  (d). 

F  =  distance  across  the  flats  =  \\d-\-  \  of  an  inch. 

D  =  distance  across  the  corners  =  (i^d -\-  -J-")  1.155. 

Fig.  35  shows  the  true  form  of  the  curves  when  the  end 
of  the  nut  is  machined  to  form  a  part  of  a  sphere  or  cone. 
This  rounding  or  bevelling  off  of  the  corners  is  calbd  cham- 
fering. The  radius  r  of  the  chamfering  is  made  from  \\d  to 
2d,  and  the  angle  a  is  made  from  60°  to  45°  with  the  axis  of 
the  nut.  When  representing  nuts  upon  a  drawing  they  should 


SCKEWS,  NUTS,  AND   BOLTS. 


always  be  drawn  to  show  the  distance  across  the  angles,  as  in 
Fig.  40. 

Exercise  5. — Draw  the  true  curves  of  a  hexagonal  nut  for 
a  bolt  6"  in  diameter  when  the  top  of  the  nut    is  chamfered 


FIG.  36. 

irt  of  a  sphere  with  a  radius  r  =  i£  times  the 
diameter  of  the  bolt  (d),  and  when  the  chamfering  is  a  pa; 


62  DRAWING  AND   DESIGNING. 

of  a  cone  the  side  of  which  makes  an  angle   of  45°  with  the 
axis  of  the  nut,  as  shown  in  Fig.  36. 

Construction. — Begin  with  the  plan,  first  locating  the  cen- 
tre c,  and  with  c  as  a  centre  and  a  radius  equal  to  \d  draw 
the  quadrant  representing  the  hole  in  the  nut,  and  from  the 
same  centre  and  a  radius  equal  to  half  the  distance  across  the 
flats  F  draw  the  quadrant  Q,  and  on  >this  quadrant  circum- 
scribe a  part  of  a  hexagon  with  the  30°  triangle  and  T  square, 
as  shown  in  Fig.  37.  Draw  the  part  elevations  and  end 
views,  and  with  r  as  a  radius  and  the  centre  on  the  centre 
line  draw  the  arc  S,  which  represents  the  spherical  chamfer, 
and  on  the  lower  elevation  draw  the  angle  a.  Divide  eb  into 
any  number  of  divisions,  say  6,  at  points  I,  2,  3,  4,  ^d. 
Where  perpendicular  lines  drawn  through  these  points  intersect 
the  arc  5  and  line  L  draw  the  horizontal  lines  7,  8,  9,  10,  1 1, 
i?f  13,  and  with  c  as  a  centre  and  radii  ci,  c2,  ^3,  ^4,  c% 
draw  arcs,  and  from  where  these  arcs  intersect  the  inclined 
face  of  the  nut  draw  vertical  lines  to  intersect  the  lines  7,  8, 
9,  10,  etc.  These  points  of  intersection  will  be  points  of  the 
curve  on  the  side  face  of  the  nut.  The  curve  of  the  front 
face  will  be  an  arc  of  a  circle.  To  find  the  curves  on  the  side 
view  draw  a  line  1 5  say  i"  below  and  parallel  to  the  lower 
face  of  the  nut  in  plan,  and  a  perpendicular  line  14  half 
an  inch  to  the  left  of  the  end  view;  where  the  arcs  drawn 
through  the  points  I,  2,  3,  etc.,  from  the  centre  c  cut  the 
inclined  face  of  the  nut  in  plan  draw  horizontal  lines  to  inter- 
sect the  line  14  ;  and  with  a  centre  at  the  intersection  of  the 
lines  14  and  15  revolve  the  lines  17,  18,  19,  20,  21,  22,  23 
on  to  the  line  15  and  draw  perpendicular  lines  through  the 
points  of  intersection.  The  line  17  revolved  will  be  the  cen- 


SCXEWS,  NUTS,  AND   BOLTS.  63 

tre  of  the  nut  face  on  the  end  view,  and  the  intersection  of 
the  lines  17,  18,  19,  20,  21,  22,  23  with  the  horizontal  lines 
7,  8,  9,  10,  11,  12,  13  will  be  points  on  one  half  of  the  re- 
quired curve.  To  complete  the  curve,  with  a  centre  at  the 
intersection  of  the  line  17  and  the  top  of  the  nut  mark  with 
the  compasses  corresponding  points  on  the  other  side  of  the 
line  17. 


FIG.  37- 

A  Conventional  Method  of  representing  large  nuts  on 
drawings  is  shown  in  Fig.  37.  In  this  representation  the 
curves  of  the  nut  are  arcs  of  circles  and  the  corners  are 
chamfered  off  at  an  angle  of  45°  to  the  axis  of  the  nut. 


64 


DRAWING  AND   DESIGNING. 


Exercise  6. — Draw  the  three  views  for  a  bolt  3"  in 
diameter.  Scale  full  size. 

Construction. — Begin,  as  in  the  last  exercise,  by  drawing 
the  plan.  Locate  the  centre  and  draw  a  circle  equal  in  di- 
ameter to  the  distance  across  the  flats  \\d-\- ^'\  on  this 
circle  with  the  set-square  circumscribe  a  hexagon,  and  find 
the  centre  of  the  side  faces  in  the  manner  shown.  Draw  the 
elevation  and  end  view  of  the  hexagon  without  the  curves. 
With  centre  a  and  radius  r'  equal  to  w  draw  the  arc  of  the 
middle  face  tangent  to  the  top  of  the  nut,  and  with  centre  b 
and  radius  r  equal  to  d  draw  the  arcs  3  to  intersect  the  lines 
I  and  2.  These  points  of  intersection  will  be  the  centres  of 
.the  arcs  of  the  side  face.  The  method  of  finding  the  centres 
of  the  curves  on  the  end  view  is  clearly  shown  on  the  draw- 
ing. Through  the  points  where  the  outside  diameter  of  the 
bolt  intersects  the  top  •  of  the  nut  with  a  radius  r*  =  d 
draw  the  arc  representing  the  bolt-point. 


/ 


A.  \ 


•-I 


FIG.  38. 


SCREWS,  NUTS,  AND  BOLTS.  65 

When  representing  small  nuts  or  nuts  drawn  to  a  small 
scale,  it  is  usual  to  make  the  distance  across  the  angles 
=  2d.  This  method  does  not  give  the  correct  proportions 
and  should  only  be  used  on  nuts  and  bolt-heads  when  d  is 
less  than  \"  in  diameter  when  drawn  to  scale.  When  nuts 
are  chamfered  on  the  upper  side  only,  it  is  usual  to  cut 
'the  corners  parallel  to  the  axis,  thus  leaving  a  cylindrical 
projection  on  the  under  side,  which  bears  on  the  piece  the 
nut  is  holding,  as  shown  in  Fig.  39. 


FIG.  39. 

The  diameter  of  the.cylindrical  projection  is  equal  to  the 
distance  across  the  flats  (\\d-\-  •§•"). 

Exercise  7 — Draw  a  hexagonal  nut  for  a  bolt  f"  in  diam- 
eter chamfered  on  the  upper  side  and  finished  on  the  under 
side  as  shown  in  Fig.  39.  Make  the  distance  across  the 
angles  =  2d,  and  draw  the  curves  by  the  method  shown  in 
Fig.  38.  Scale  full  size. 

Construction. — Draw  the  semicircle  I,  2  and  divide  it  into 


66  DRAWING  AND  DESIGNING. 

three  equal  divisions  at  the  points  i,  2,  3,  4;  through  these 
points  draw  perpendicular  lines  to  intersect  the  top  of  the 
nut.  The  method  of  finding  the  centres  of  the  arcs  of  the 
side  faces  will  be  clearly  understood  from  Fig.  38,  where  r 
is  in  each  case  =  d. 

Machine  fastenings  are  most  commonly  effected  by  means 
of  bolts,  keys,  or  rivets.  When  two  or  more  pieces  have  to' 
be  held  together  with  the  intention  of  disconnecting  them 
again,  a  bolt  or  key  is  used;  the  rivet  being  used  only  when 
the  connection  is  to  be  permanent.  The  most  common  form 


FIG.  40. 

01  oolt  used  in  general  machine  construction  is  the  hexagonal* 
headed  bolt  shown  in  Fig.  40. 

Exercise  8 — -Draw  a  hexagonal  headed  bolt  and  nut  in 
position  on  a  cast-iron  pipe-flange  (Fig.  41).  Make  the  bolt 
J"  in  diameter.  Scale  full  size. 

Construction.  —  First  draw  the  lines  representing  the 
thickness  of  the  pipe  and  flanges.  The  angles  of  the  nut 
should  be  clear  of  the  fillet  about  \"  and  the  radius  (r)  should 
be  at  least  -J".  Therefore,  the  distance  (b)  will  be  equal  to 
half  the  distance  across  the  angles  of  the  nut  +  i"  +  r.  To 
give  the  flange  a  proper  finish,  the  distance  (a)  is  made  from 


SCREWS,   NUTS,    AND   BOLTS.  O/ 

•J"  to  1"  greater  than  half  the  distance  across  the  angles  of  the 
nut.    The  number  of  threads  per  inch  will  be  found  in  Table  8. 


FIG.  41. 

The  Square-headed  Bolt. — Fig.  42  is  a  cheaper  make 
than  the  hexagonal  and  is  generally  used  in  structures  of 
rough  iron.  It  is  sometimes,  however,  adopted  in  machine- 
and  engine-construction  generally  when  the  head  is  let  into  a 
recess,  as  shown  in  Fig.  42.  It  is  used  in  this  instance  in 
preference  to  the  hexagonal  head,  because  it  is  easier  to 
make  the  square  recess  in  the  pattern.  In  Fig.  42,  it  is 
shown  in  combination  with  a  square  nut,  the  sides  of  which 
give  a  better  gripping  surface  for  the  wrench  than  the 
hexagonal,  but  the  latter  can  be  screwed  up  in  a  more  con- 
fined position,  as  it  is  only  necessary  to  turn  it  through  an 
angle  of  60°  to  get  the  wrench  or  spanner  on  to  the  next 
two  parallel  faces;  while  the  square  nut  has  to  be  turned 
through  an  angle  of  90°  under  the  same  conditions. 


68  DRAWING   AND    DESIGNING. 

TABLE 

UNITED    STATES    STANDARD    OF 
Screw-threads. 


Diameter 
of 
Screw. 

Number 
of 
•       Threads 
per  Inch. 

Diameter 
at 
Bottom 
of 
Threads. 

Area  at 
Bottom 
of 
Threads  in 
Square  Inches. 

Area  of 
Bolt  Body 
in 
Square  Inches. 

X 

r 

20 
18 
16 

.185 
.240 
.294 

.027 
•045 
.068 

.049 
.077 
.110 

7/16 

14 

•344 

•093 

.150 

% 

13 

.400 

.126 

.196 

9/16 

12 

•454 

.162 

•249 

M 

II 

.507 

.202 

•307 

# 

10 

.620 

•  302 

.442 

ft 

9 

•731 

.420 

.601 

i 

8 

.837 

•550 

.785 

i# 

7 

.940 

.694 

•994 

iX 

7 

.065 

.893 

1.227 

i/s 

6 

.160 

1-057 

1.485 

1/2 

6 

.284 

1.295 

1.767 

I# 

5^ 

-389 

I.5I5 

2.074 

i* 

5 

.491 

1.746 

2.405 

.i# 

3 

.616 

2  .  05  1 

2.761 

2 

4X 

.712 

2.3O2 

3.142 

*% 

4^ 

.962 

3-023 

3.976 

2/2 

4 

2.176 

3-7I9 

4.909 

2^ 

4 

2.426 

4.620 

5-940 

3 

3X 

2.629 

5.428 

7.069 

3X 

;  3^ 

2.879 

6.510 

8.296 

3X 

3X 

3.100 

7.548 

9.621 

3M 

3 

3-3I7 

8.641 

11.045 

4 

3 

3-567 

9-963 

12.566 

4X 

2^ 

3.798 

II.329 

14.186 

4^ 

2^ 

4.028 

12-753 

15.904 

4U 

2^. 

4.256 

14.226 

I7-72I 

5 

2^ 

4.480 

15.763 

I9-635 

5X 

2^ 

4.730 

17.572 

2T.648 

5^     ' 

2/8 

4-953 

19.267 

23.758 

5X 

2/8 

5-203 

21.262 

25-967 

6 

2X 

5-423 

23.098 

28.274 

NOTE. — The  above  table  gives  the  sizes  of  the  rough  nuts  and  bolt-heads.    The  finished 


SCREWS,   NUTS,  AND    BOLTS. 


69 


8. 

SCREW-THREADS,  BOLTS,  AND    NUTS. 


Nuts. 

Heads. 

Tap  Drill. 

m 

t£fH 

hA  J 

i 

FhH 

0 

^5 

@ 

1         | 

X 

5/i6 

7/!a 

9/16 

19/32. 
11/16 
25/32 

3i/3« 

37/64 

51/64 
9/10 

i 

§ 

7/10 

10/12 
63/64 

i 

5/16 

f 

X 
19/64 
11/32 
25/64 

7/16 
31/64 

rr 

23/32 

3£6 

5/i6 
23/64 
13/32 
15/32 
17/32 

fi 

i 

2 
*ft 

2 

1 

2¥- 

s 

3H 

i, 
i/ 

13/16 
29/32 
i 

«A 

27/32 
3si/32 

2 

2X 

4X 

4iV 

m 

4« 
4H 
SH 

6 

2 

2^ 
2X 

1 

1 

3 
3X 

r 

5}| 

6H 

1 

& 

3X 

2T* 

2|1 
2^ 

1 

4 
4X 

7X                Hi 

I 

ll 

4X 

3TV 

3X 

3H 

1 

4A 

b 

5X 
6 

8 

ill 

ijf 

sX 

5X 
6 

4 

4X 

sS 

sizes  are:     H=d-i/i6"; 


>";    A=//-i/i6";    A!  =  — 


DRA  WING  AND   DESIGNING. 


Exercise  9. — Draw  a  bolt  with  a  square  head,  and  nut,  as 
shown  in  Fig.  42.  Make  the  bolt  i"  in  diameter.  Scale 
full  size. 

Construction. — The  proportions  of 
heads  and  nuts  will  be  found  in  Table 
8.  The  radius  (r)  is  made  equal  to  F 
and  tangent  to  the  top  of  the  nut  or 
head. 

A  Stud-bolt  consists  of  a  bar 
screwed  at  both  ends  (Fig.  43),  one 
end  being  screwed  into  the  piece  upon 
which  the  connection  is  made.  The 
other  piece  is  then  passed  over  the 
studs  and  secured  by  a  nut.  To  allow 
the  nut  to  make  a  tight  joint,  the 
length  of  the  body  or  plain  part  must 
always  be  less  than  the  thickness  of 
the  piece  into  which  it  passes. 

Studs    are    used    only    when    it    is 
impossible,    or  at  least  very   inconve- 
nient, to  use  an  ordinary  bolt.      When  FlG-  42. 
studs  are  screwed  into  cast  material,  the  screwed  part  should 
extend  into  the  metal  at  least   ij  times  their  diameter,  and 


FIG.  43. 

shoidd  never    be  allowed  to  bear  on  the  bottoms  of  the  holes. 
Fig.  44  shows  a  stud  used  to  secure  the  cylinder-cover  (c)  to 


SCREWS,  NUTS,  AND   BOLTS. 


D  R 


FIG.  44. 


/2  DKA  WING  AND   DESIGNING. 

the  cylinder.  Studs  are  preferred  to  bolts  for  this  purpose 
because  the  flanges  can  be  made  very  much  smaller,  and  the 
cover  can  be  removed  and  replaced  without  disturbing  the 
cylinder-lagging.  A  stud  should  not  be  placed  nearer  to  the 
edge  of  the  metal  than  a  distance  equal  to  (d)  measured 
from  the  centre  of  the  stud,  and  in  steam-tight  joints  it  is 
usual  to  make  the  distance  (a)  equal  to  ij<^,  as  shown  in 
Fig.  44. 

Fig.  43  shows  the  form  of  stud  in  general  use.  The 
body  of  this  stud  is  made  cylindrical  and  equal  in  diameter 
to  the  diameter  of  the  screw.  As  the  weakest  part  of  the 
stud  is  at  the  change  of  section,  the  form  of  stud  shown  in 
Fig.  44,  if  subjected  to  a  greater  stress  than  it  could  with- 
stand, would  break  off,  leaving  the  screwed  part  in  the  metal, 
but  by  cutting  a  semicircular  groove  of  a  depth  —  the  depth 
of  the  thread  on  the  end  of  the  body  that  comes  in  contact 
with  the  piece  into  which  the  stud  is  screwed,  as  in  Fig.  43, 
this  part  is  'strengthened  and  the  stud  would  then  break 
where  the  upper  screwed  part  joins  the  body.  The  broken 
stud  can  then  be  easily  removed  by  means  of  a  pipe-wrench. 


FIG.  45. 

In  Fig.  45,  the  stud  has  a  square  body  which  serves  as  a 
shoulder,  against  which  the  stud  may  be  screwed  up  tight  by 
means  of  a  wrench  applied  to  the  square  part.  Studs  with 
round  bodies  are  screwed  into  position  by  means  of  a  tool 


SCREWS,  NUTS,  AND   BOLTS. 


73 


called  a  stud-nut ;   this  consists  of  a  long  nut  fitted  with  an 
internal  screw,  as  shown  in  Fig.  46.     To  avoid  damaging  the 


FIG.  46. 

point  of  the  stud,  the  bottom  of  the  screw  in  the  stud-nut  is 
lined  with  copper.  By  applying  a  wrench  to  the  stud-nut, 
the  stud  can  be  screwed  into  the  tapped  hole  in  the  metal 
until  stopped  by  the  plain  portion  on  the  stud.  The  stud- 
nut  can  then  be  removed  by  a  quick  turn  back. 

Exercise  10. — Draw  a  section  of  a  steam-cylinder  end- 
flange,  showing  the  method  of  securing  the  cylinder-cover  or 
head  (c)  to  the  cylinder  (Fig.  44).  Scale  full  size. 

When  a  bolt-head  is  of  such  form,  or  in  a  position  in 
which  it  cannot  be  held  with  a  wrench  to  keep  it  from  revolv- 
ing when  screwing  up  the  nut,  the  bolt  is  provided  with  some 


'ywi«p 

FIG.  47.  FIG.  48. 

device  in  the  body  to  overcome  the  difficulty.  The  spherical 
or  button-headed  bolt,  shown  in  Fig.  47,  is  provided  with  a 
square  part  under  the  head,  which  fits  into  a  corresponding 
hole  in  the  material  through  which  it  passes.  Another  de- 


74 


DRAWING   AND    DESIGNING. 


sign  used  for  the  same  purpose  is  shown  in  Fig.  48 ;  this  is 
called  a  snug,(  and  consists  of  one  or  two  projections  forged 
on  the  neck  of  the  bolt  and  made  to  fit  a  correspondingly 
shaped  hole  in  the  metal. 

Fig.  49  shows  a  bolt  with  a  countersunk  head  and  nut. 
The  bolt  is  kept  from  revolving  by  a  pin  (/),  which  is  driven 
into  a  hole  drilled  in  the  body  of  the  bolt  close  to  the  head. 
The  projecting  part  of  the  pin  fits  into  a  recess  cut  to  receive 
it.  The  nut  is  provided  with  holes  to  receive  the  spanner 
used  in  screwing  it  up,  and  may  be  made  equal  in  diameter  to 
half  the  amount  of  metal  between  the  bottoms  of  the  threads 


FIG.  49. 

and  the  outside  of  the  nut.  The  depth  of  the  holes  may  be 
made  .25  of  //,  the  height  of  the  nut.  The  projecting  part  of 
the  pin  (/)  is  usually  made  square  and  equal  to  .25^.  The 
pin  (/)  is  sometimes  screwed  into  the  bolt  to  avoid  its  being 
lost  when  the  bolt  is  withdrawn. 

The  T-headed  Bolt  shown  in  Fig.  50  has  the  sides  of 
the  head  level  with  the  square  neck  or  body  of  the  bolt,  and 
is  used  where  there  is  not  sufficient  room  to  use  bolts  of  the 
hexagonal  or  square-headed  form.  A  common  application  of 
this  form  of  bolt  is  shown  in  Fig.  50. 


SCREWS,  NUTS,  AND   BOLTS, 


75 


The  Tap-bolt  shown  in  Fig.  5 1  makes  a  fastening  with- 
out the  use  of  a  nut.  The  bolt  is  screwed  into  a  tapped 
hole  in  one  of  the  pieces  to  be  connected,  while  the  head 


FIG.  50.  FIG.  51. 

presses  on  the  other  piece.  This  form  of  bolt  is  used  in 
place  of  a  stud  where  the  piece  to  be  connected  could  not,  if 
studs  were  used,  be  passed  over  the  projecting  studs,  as  in  a 
pipe-fastening  where  two  of  the  faces  are  at  an  angle  to  each 
other. 

There  is  no   standard   for  the    foregoing  bolt-heads  and 
nuts,  but  the  following  proportions  are  in  general  use: 


//  =  .;</,     H=d,     n  =  .6d,     /  =  \\d. 

Exercise  u  —  Draw  a  spherical  or  button-headed  bolt  with 
a  square  neck;  and  a  head  with  a  snug  on  the  neck,  as  shown 
in  Figs.  47  and  48.  A  counter  sunk-  headed  bolt  with  a  counter- 
sunk nut  as  shown  in  Fig.  49,  a  T-headed  bolt  with  a  square 


76 


DRA  WING  AND   DESIGNING. 


neck,    as    shown    in    Fig.    50,    and    a   tap-bolt,   as    shown   in 
Fig.  51.      Make  d  in  each  case  —  \" .      Scale  full  size. 

Hook-bolt. — This  form  of  bolt  is  used  where  it  is  im- 
possible or  undesirable  to  have  bolt-holes  through  one  of  the 
connected  pieces.  A  common-  application  of  this  bolt  is 
fastening  pieces  (such  as  hangers)  to  flanged  beams,  as  shown 
in  Fig.  52.  To  keep  the  bolt  from  turning,,  the  body  is 


DR 


FIG.  52. 

made  square  in  cross-section  and  passes  into  a  correspond- 
ingly shaped  hole  in  the  connected  piece.  The  diameter  of 
the  screw  is  equal  to  the  square  body. 

Exercise  12 — Draw  an  ELEVATION  of  a  hook-bolt,  fasten- 
ing a  piece  to  a  flanged  beam,  as  shown  in  Fig.  52,  and 
PLAN  of  the  bolt  only,  looking  down  on  the  bolt  head.  Scale 
full  size. 


SCREWS,  NUTS,  AND    BOLTS. 


77 


Tapered  Bolts  are  used  to  facilitate  fitting  where  it  is 
necessary  that  the  bolt  should  be  a  perfect  fit  in  the  hole. 
Fig.  53  shows  a  tapered  bolt  that  is  in  common  use  in  the 
couplings  of  propeller-shafts  of  steamships.  As  coupling- 
bolts  have  only  to  resist  the  shearing  force,  caused  by  the 
twisting  strain  on  the  shaft,  the  diameter  of  the  bolt  is 


FIG.  53- 

the  diameter    on  the  line  where    the  two  flanges    come    to- 
gether,  and  its  strength  is  equal  to  -  —fs. 

4 

As  the  screwed  part  of  the  bolt  has  only  to  resist  the 
tension  due  to  screwing  up,  this  part  is  made  smaller  in 
diameter  than  the  small  end  of  the  tapered  part.  In 
practice,  the  diameter  of  the  screwed  part  is  generally 


made    equal   to 


and    the    height    of    the    nut    from 


i"  to  \"  less  than  the  diameter  of  the  screw.  The  advan- 
tages gained  by  using  tapered  instead  of  parallel  bolts  for 
couplings  are :  they  can  be  made  a  perfect  fit  in  the  hole, 
which  insures  that  the  different  lengths  of  shaft  are  in 
better  alignment,  are  easier  withdrawn,  and,  owing  to  the 
diameter  of  the  screw  being  much  smaller  than  the  diam- 
eter at  the  junction  of  the  shafts  (i.e.,  the  effective  diam- 
eter), the  flanges  can  be  made  smaller. 

Exercise    13. — Draw  a  tapered  bolt    for    a    marine  shaft- 


78  DRAWING  AND   DESIGNING. 

coupling,  showing  a  part  of  the  shaft-flanges,  to  the  dimen- 
sions given  in  Fig.  53.  Scale  half  size. 

Construction. — Draw  the  centre  line  of  the  bolt,  then  the 
line  showing  the  junction  of  the  flanges,  and  on  this  line 
mark  off  the  diameter  of  the  bolt.  From  the  point  (a)  draw 
the  line  ab  12  inches  long  and  parallel  to  the  axis  of  the 
bolt,  and  from  b  draw  be  perpendicular  to  ab  and  -fa"  long, 
join  ac  which  makes  the  required  taper.  The  radius  (r)  is 
equal  to  the  diameter  of  the  bolt  at  the  large  end. 

Exercise  14 — Draw  a  tapered  bolt  as  in  the  preceding 
exercise,  leaving  off  the  parts  of  the  shafts,  and  making  the 
diameter  of  the  bolt  3  inches,  and  the  length  of  the  body 
equal  to  8  inches.  Scale  half  size. 

Foundation-bolts. — This  class  of  bolts  is  employed  for 
fastening  engine-  and  machine-frames  to  stone,  brick,  or  con- 
crete foundations. 

The  Rag-bolt  (Fig.  54). — This  form  of  bolt  is  fastened 
to  stone  by  cutting  a  Lewis  hole,  which  increases  in  size  as 
it  descends.  The  small  end  of  the  hole  is  made  from  J"  to 
\"  larger  than  the  large  end  of  the  bolt-head.  After  the 
bolt-head  is  placed  in  the  hole,  the  space  between  it  and  the 
sides  of  the  hole  is  filled  with  molten  lead  or  sulphur,  thus 
securing  the  bolt  firmly  in  position.  The  frame  is  cast  with 
a  projecting  foot  through  which  a  hole  is  cored.  This  foot 
passes  over  the  foundation-bolt  and  the  engine-  or  machine- 
frame  is  held  in  position  by  the  pressure  of  the  nut.  The 
diameter  of  the  hole  through  the  foot  is  =  d -\-  J".  The 
diameter  of  the  washer  w  is  equal  to  2d  -\-  \" ,  and  the  thick- 
ness ^V  °f  d'  The  distance  a  is  =  half  the  diameter  of  the 
washer  -\-  f".  The  section  of  the  bolt-head  is  oblong  and 


SCREWS,  NUTS,  AND  BOLTS. 


79 


D.R. 


FIG.  54- 


8O  DRAWING  AND   DESIGNING. 

purposely  made  rough  and  jagged,  which  obviously  increases 
the  resistance  the  bolt  offers  against  being  withdrawn  from 
the  hole.  The  length  L  of  the  head  (h)  is  -usually  made 
equal  to  6d  and  has  a  taper  =  \\"  per  foot. 

Exercise  15 — Draw  a  rag-bolt  in  elevation  and  plan  with 
a  part  of  a  cast-iron  engine-frame  as  shown  in  Fig.  54, 
making  (d)  —  ij"  in  diameter.  Scale  full  size. 

Construction. — Draw  the  centre  line  and  the  line  repre- 
senting the  top  of  the  stone  foundation,  then  mark  off  to  (b) 
the  distance  which  the  beginning  of  the  head  is  below  the 
level  of  the  top  of  the  foundation,  and  from  the  point  (b) 
find  the  taper  on  one  side  of  the  axis  in  the  same  manner  as 
in  Exercise  13.  Make  the  top  of  the  hole  de  J"  greater  than 
the  large  end  of  the  bolt-head,  and  through  (e)  draw  a  line 
parallel  to  the  side  of  the  bolt-head  be,  which  will  represent 
the  edge  of  the  hole.  To  complete  the  other  side  of  the 
bolt-head  mark  off  with  the  dividers  equal  distances  on  the 
other  side  of  the  centre  line. 

The  Lewis  Bolt,  shown  in  Fig.  55,  is  used,  in  some 
cases,  in  preference  to  the  rag-bolt,  because  it  can  be  much 
more  easily  removed,  which  is  accomplished  by  withdrawing 
the  key  K.  The  side  be  of  the  bolt-head  (//)  has  a  taper  of 
1-t/'  per  foot,  while  the  opposite  side  is  parallel  to  the  axis 
of  the  bolt.  The  length  L  of  the  head  may  be  made  as  in 
the  design  of  the  rag-bolt,  equal  to  6d. 

In  Fig.  55,  the  bolt  is  shown  holding  down  the  pedestal 
shown  in  Fig.  54,  page  79.  The  hole  that  the  bolt  passes 
through  is  rectangular,  to  allow  the  pedestal  to  move 
laterally.  The  proportions  of  the  washer  are  the  same  as  in 
the  last  exercise.  The  thickness  (/)  of  the  key  is  made 


SCREWS.  NUTS,  AND  BOLTS. 


81 


D.R. 


FIG.  55- 


82  DRAWING  AND   DESIGNING. 

sufficient  to  allow  the  large  end  of  the  bolt-head  to  pass 
through  the  small  end  of  the  hole  +  £"  for  clearance,  and 
the  point  should  stop  from  £"  to  \"  up  from  the  bottom  of 
the  hole.  The  length  of  the  key-head  is  made  equal  to  2/, 
and  its  thickness  equal  to  t. 

Exercise  16 — Draw  an  ELEVATION  of  a  Lewis  bolt  show- 
ing the  method  of  securing  it  to  the  foundation,  a  section  of 
pedestal-base  and  a  PLAN  showing  the  shape  of  the  hole 
through  which  the  bolt  passes,  as  in  Fig.  55.  Draw  also  an 
END  VIEW  of  the  bolt  leaving  out  the  foundation-stone  and 
pedestal-base.  Make  d  =  2"  in  diameter.  Scale  half  size. 

Construction. — Proceed  in  the  same  manner  as  in  the 
previous  exercise.  The  distance  (a)  in  this  case  should  be 
equal  to  the  diameter  of  the  washer  (w)  -f-  the  longitudinal 

movement    +  \" .       Make    e  =  -  +  2",   /=  d -\-    half    the 

w 
longitudinal  movement,  r  = 1-  J" ' . 

Anchor-bolts  passing  through  the  foundation  are  recom- 
mended in  preference  to  the  rag  or  Lewis  bolts  wherever  it 
is  possible  to  use  them.  The  heads  are  made  removable,  so 
that  the  bolts  can  be  inserted  from  the  top,  and  are  either 
under  the  foundation  or  in  a  recess  on  the  side,  as  in  Fig.  56. 
The  simplest  form  of  removable  head  is  made  by  screwing 
a  nut  upon  the  lower  end  after  the  bolt  is  in  position  and 
driving  a  split  pin  through  it  to  keep  it  from  working  loose. 
The  objection  to  this  form  of  head,  however,  is  that  the  nut 
cannot  be  removed  without  difficulty  after  it  has  been  in 
place  long  enough  to  rust.  The  usual  and  most  suitable 
form  of  removable  head  for  this  class  of  foundation-bolt  is 


SCREWS,  NUTS,  AND   BOLTS. 


DR. 


FIG.  56. 


84  DRAWING  AND  DESIGNING. 

shown  in  Fig.  56.  In  this  design  the  head  end  is  made 
square  in  section,  and  has  a  rectangular  hole  into  which  the 
cotter  C  is  fitted.  The  bolt  is  kept  from  turning  when  the 
nut  is  being  screwed  up  by  the  square  end  fitting  into  a 
corresponding  hole  in  the  washer  W.  To  keep  the  cotter  C 
from  working  out  of  place  it  is  provided  with  gib-heads  at 
the  ends.  As  the  strength  of  a  bolt  in  tension  is  due  to  the 
area  at  the  bottom  of  the  thread,  the  body  of  the  bolt  may 
be  reduced  to  this  extent  without  reducing  its  strength. 

The  proportions  of  the  cotter  and  the  bolt-end  through 
which  the  cotter  passes  are 

bl  for  shear  would  =  — ,  but  owing  to  the  uncertainty  of  the 

longitudinal  shearing  resistance  of  the  material,  it  is  usual  in 
practice  to  make  it  equal  S,  which  insures  ample  strength. 
The  length  /  of  the  cotter  should  not  be  less  than .28  +  J" 
and  is  usually  made  =  35,  which  gives  a  better  support  to 
the  washer  W.  The  washer  W  is  usually  made  round  or 
square.  When  round,  D,  the  diameter,  will  be  found  by  the 
formula 

=&-3& (L 


from  which  D  = 


The    value    of  fc    may   be    taken  =  4    tons   and  allow  a 
factor  of  safety  of  20.      Take  the  value  of/,  in   this  case  =  7 


SCREWS,    A'C/TS,    AND    BOLTS.  8$ 

tons  per  square  inch.  The  thickness  T'ol  the  washer  is  made 
from  d^  to  \\d. 

Exercise  17 — Draw  an  ELEVATION  of  an  anchor-bolt  for 
securing  an  engine-frame  to  a  stone  foundation  showing  the 
frame-foot  and  stonework  in  section;  the  top  stone  of  sand- 
stone and  the  under  part  of  brick,,  Make  also  an  END  VIEW 
of  the  bolt-head  with  the  cotter  in  section.  Make  d  =  ij", 
L  =  6'  o",  a  =  </+  J",  e  =  2d  +  ±" '.  Scale  half  size. 

Cap-screws,  the  different  forms  of  which  are  shown  in 
Fig.  57,  are  employed  like  the  tap-bolt  for  screwing  two 
or  more  pieces  together.  The  reason  for  the  name  *'  cap- 
screws  "  is  that  they  are  used  for  fastening  on  caps  or  covers 
on  machinery,  such  as  the  caps  of  journal-bearings,  etc. 

The  Length  of  a  cap-screw  is  the  distance  under  the 
head,  excepting  the  flat-headed  form,  which  includes  the 
thickness  of  the  head  in  the  length.  The  angle  of  the  cone 
of  the  flat-headed  screw  is  about  76°,  the  sides  making  angles 
of  52°  with  the  top,  but  it  is  usual  to  represent  the  heads  on 
the  drawings  with  the  sides  making  an  angle  of  60°  with  the 
top. 

The  height  of  the  flat-headed  screw  is  =  .7  of  the  screw 
diameter.  The  height  of  the  button-headed  screw  =  .6  of 
the  screw  diameter.  The  width  of  the  saw-cuts  on  the  heads 
are  =  .2  of  the  screw  diameter.  The  other  proportions  are 
given  in  Table  9. 

Collar-screws  are  used  for  the  same  purpose  as  cap- 
screws.  The  collar  under  the  head,  Fig.  58,  gives  a  larger 
bearing-surface  for  the  head  and  is  used  where  the  hole 
through  the  connected  piece  is  larger  than  the  screw 
diameter. 


86 


.DRAWING  AAD   DESIGNING. 


TABLE   9. 

CAP-SCREWS. 
(WORCESTER  SCREW  Co.) 

Hexagon  and  Square  Heads. 


Diameter  1 
of  screw  f 

Threads     ) 
to  inch  f 

% 
20 

5/16 
18 

/8 

16 

7/16 
14 

# 

12 

9/16 

12 

# 

II 

X 
10 

% 

9 

i 
8 

1/8 

7 

iX 

7 

Hexagon  Head. 


Diameter  1 
of  head  f 

7/ie 

A* 

9/ie 

>     jHj 

X 

13/16 

/« 

I 

t* 

* 

~>y* 

•K 

Length       I 
of  head  \ 

X 

5/i6 

/8 

7/16 

'/2 

9/16 

* 

M 

y* 

i 

iX 

i* 

Square  Head. 

Diameter  I 
of  head  f 

/8 

7/16 

# 

9/16 

X 

11/16 

M 

H 

r'A 

* 

iX 

IK 

tji 

Length      (_ 
of  head  | 

X 

5/i6 

/8 

7/16 

'A 

9/16 

J 

*_ 

X 

1 

ll/s 

iX 

iK 

Flat,  Round,  Fillister,  and  Button  Heads. 


Diameter  | 
of  screw  \ 

/8 

3/i6 

X 

5/i6 

/8 

7/16 

% 

9/16 

N 

X 

^ 

i 

Threads     ). 
to  inch  \ 

40 

24 

20 

18 

16 

14 

12 

12 

II 

IO 

9 

8 

I 

Flat  Head. 


Diame'er  I 
of  head  f 

X 

/8 

15/32 

^ 

X 

13/16 

ft 

I 

I/ 

1/8 

Round  and  Fillister  Heads. 


i 

Diameter  1 
of  head  f 

3/i6 

X 

/8 

7/16 

9/16 

^ 

X 

13/16 

^ 

i 

i^ 

iX 

Length  I 
of  head  f 

# 

3/i6 

X 

5/i6 

/8 

7/16 

# 

9/i6 

H 

X 

N 

i 

Button  Head. 


Diameter  ) 
of  head  | 

7/32 
Full 

5/i6 

7/16 

9/i6 

H 

X 

13/16 

15/16 

i 

iX 

SCREWS,  NUTS,  AND  BOLTS. 

CAP  SCREWS. 


FIG.  58. 

Set-screws  are  employed  to  hold  parts  of  machines  in 
place  by  setting  the  point  of  the  screw  against  the  object  to 
be  held. 


DRAWING  AND  DESIGNING. 


The  Holding  Power  of  Set-screws. — In  tests  (made 
by  G.  Lansa,  A.S.M.E.)  of  the  holding  power  of  set-screws 
for  securing  pulleys  to  steel  shafts  by  means  of  wrought-iron 
screws  with  points  of  the  form  shown  at  Nos.  I,  2,  and  3 
(Fig.  59).  It  was  found  that  the  round-pointed  form  (No.  i), 
with  the  radius  of  the  point  equal  to  about  the  diameter  of 
the  screw,  had  the  greatest  holding  power.  The  cup-point 
(No.  2),  which  was  case-hardened,  held  well  while  the  edges 
were  sharp,  but  the  holding  power  decreased  after  the  first 
test  because  of  the  edges  becoming  flat.  This  serves  to 
show  that  to  get  good  results  with  this  form  of  point  the 
screw  must  be  made  of  a  harder  material  than  that  of  the 
piece  it  is  holding,  and  should  not  be  used  where  the  point 
is  subjected  to  excessive  wear. 

The  length  of  the  head  and  the  distance  across  the  flats 
is  equal  to  the  diameter  of  the  screw.  The  diameters  of 
the  round  and  flat  pivot-points  (No.  8)  are  equal  to  the 
diameter  at  the  bottom  of  the  threads,  and  the  length  of 
point  =  from  .5^  to  d.  The  angle  of  the  cone  and  hanger 
set-points  is  usually  45°  or  60°. 

Strength  of  Bolts. — In  an  ordinary  bolt  with  a  V  thread 
employed  for  holding  two  or  more  pieces  together  by  the 
pressure  due  to  the  screwing  up  of  the  nut,  the  bolt  would 
yield  (i)  by  tension  combined  with  a  torsional  stress  due  to 
the  friction  between  the  threads  of  the  nut  and  those  of  the 
bolt.  This  combination  of  tension  and  torsion  causes  the 
bolt  to  part  where  the  thread  ends,  because  of  the  rapid 
change  of  section;  (2)  by  shearing  off  the  threads;  (3)  by 
shearing  off  the  bolt-head.  Comparing  (i)  with  (2)  it  will  be 
found  that  the  shearing  strength  of  the  thread  on  the  nut  is 


SCREWS,  NUTS,  AND  BOLTS. 
\\ 


89 


No.   i.  Regular  round  point,  set. 

'     2.  Cup  point,  set. 

'     3.  Flat     " 

'     4.  Cup     "        headless. 

5.  Round  point,  headless. 

4     6.  Cone         "  " 


FIG.  59. 

SET-SCREWS. 

No.   7.   Flat,  pivot  point. 


8.  Round,  " 

9.  Hanger,  set 

10.  Cone  point. 

11.  Necked  style. 


Diameter  i 
of  screw  f 

Threads     | 
to  inch  f 

X 

20 

5/i6 

18 

H 
16 

7/16 
14 

12 

12 

X 

II 

10 

ft 

9 

i 
8 

1/8 

7 

7 

go  DRAWING  AND  DESIGNING. 

equal  to  about  twice  the  strength  of  the  section  at  the 
bottom  of  the  thread,  but  in  practice  it  is  found  that  when 
the  depth  of  the  nut  is  made  less  than  .7  of  the  bolt 
diameter,  the  threads  are  injured.  Bolts  or  studs  used  for 
face-joints  on  vessels  subjected  to  internal  pressure,  depend 
upon  the  care  exercised  by  the  workman  to  leave  sufficient 
strength  to  withstand  the  pressure  after  the  bolt  is  screwed 
up.  As  the  amount  of  strength  left  is  an  unknown  and 
uncertain  quantity,  the  stress  upon  the  bolts  calculated  from 
the  internal  pressure  should  be  kept  very  low,  and  no  face- 
joints,  unless  very  small  ones,  should  have  bolts  less  than  •£" 
in  diameter.  In  permanent  joints  the  stress  thus  calculated 
per  square  inch  of  section  of  bolt  at  the  bottom  of  thread 
should  not  exceed  6000  Ibs.  ;  and  for  bolts  in  joints  frequently 
broken  the  stress  should  be  as  low  as  2000  Ibs.  Thus  </,  , 
the  diameter  at  the  bottom  of  the  thread,  to  withstand  the 
required  pressure,  will  be  found  by  the  formula 


X  a 


a  =  area  of  exposed  surface  in  square  inches; 
/  =  the  pressure  per  square  inch; 
n  =  the  number  of  bolts; 
ft  =  the  strain  per  square  inch; 

Unwin's  formula  for  cylinder-bolts  or  studs  is 


SCREWS,  NUTS,  AND  BOLTS.  gi 

D  =  the  diameter  of  the  cylinder; 
p  =  the  pressure  per  square  inch; 
n  =  the  number  of  bolts. 

/  =  the  strain  per  square  inch  =  2000  Ibs.  when  the 
diameter  of  the  cylinder  is  10"  or  less,  and 
4000  Ibs.  when  above. 

Cylinder-cover  and  steam-chest  cover-bolts  should  be  of 
soft  steel. 

Bolts  of  Uniform  Strength. — When  a  bolt  in  tension  is 
subjected  to  irregular  strains  and  heavy  vibrations,  it  is  made 
lighter  and  stronger  by  making  the  area  of  the  cross-section 
of  the  unscrewed  part  equal  to  that  of  the  screwed  part  at 
K  the  bottom  of  the  threads.  This  is  obtained  by  turning 
down  the  bolt-body  to  the  same  diameter  as  the  screwed  part 
at  the  bottom  of  the  threads,  leaving  a  part  at  each  end  to 
fit  the  hole,  as  shown  in  Fig.  60. 


FIG.  60. 


Another  method  adopted  where  it  is  necessary  that  the 
bolt  should  fill  the  hole  it  is  fitted  into,  is  to  drill  a  hole 
through  the  centre  of  the  bolt  from  the  head  up  to  where  the 
screw  ends,  as  shown  in  Fig.  61. 

The  diameter  of  the  hole  is  found  by  the  formula 


=  Vd*  - 


(15) 


92 


DRAWING  AND   DESIGNING. 


where  d^  =  diameter  of  the  bolt; 

d  =  outside  diameter  of  the  bolt-body; 

dl  =  the  diameter  at  the  bottom  of  the  thread, 


D.R. 

FIG.  61. 

Nut-locking1  Devices. — The  pitch  of  the  threads  on  screw 
fastenings  is  such  that  nuts  subjected  to  constant  pressure 
will  not  slack  back  because  of  the  frictional  holding  power 
between  the  threads  of  the  nut  and  those  of  the  bolt  com- 
bined with  the  friction  between  the  bearing-surface  of  the 
nut  and  the  piece  it  is  fastening.  If,  however,  the  pressure 
is  intermittent  and  there  is  much  vibration,  the  nut  will  slack 
back  when  the  load  on  it  has  been  sufficiently  reduced  to 
allow  the  vibrations  to  overcome  the  friction  which  opposes 
the  turning  of  the  nut.  Consequently,  wherever  a  screw  is 
subjected  to  much  vibration  and  a  varying  load,  the  nut  will 
gradually  slack  back  and  allow  the  connection  to  work  loose 
unless  some  locking  device  is  used  to  keep  the  nut  from 
rotating  backward. 

A  Jam-nut  is  the  simplest  and  most  frequently  employed 
device.  This  is  simply  a  second  nut  N  (Fig.  62)  screwed 
down  on  the  top  of  the  lower  nut  L  as  tightly  as  possible, 
and  the  lower  nut  turned  back  to  cause  the  threads  in  the 
nut  N  to  press  upon  the  under  side  of  the  threads  on  the 
bolt,  while  the  threads  in  the  nut  L  press  upon  the  upper 


SCREWS,  NUTS,  AND   BOLTS. 


93 


side  of  the  bolt-threads.  Hence  all  slack  between  the 
threads  of  the  bolt  and  those  of  the  nuts  is  taken  up  and  the 
nuts  will  have  a  frictional  holding  power  independent  of  the 


FIG.  62. 

tension  on  the  bolt.  By  this  arrangement  the  load  on  the 
bolt  is  carried  on  the  upper  nut,  which  should  be  the  larger. 
In  practice,  however,  the  thin  nut  is  often  put  on  the  top 
because  when  screwed  down  first  it  requires  a  special  spanner 
to  turn  it  without  disturbing  the  upper  nut,  the  ordinary 
spanner  or  wrench  being  too  thick.  The  general  rule  is  to 
make  the  thin  nut  equal  to  half  the  diameter  of  the  bolt,  but 
many  engineers  use  two  ordinary  nuts,  thus  making  the 
height  of  the  nuts  equal  to  twice  the  diameter  of  the  screw. 
Others  again  make  a  compromise  between  these  methods  and 
make  the  height  of  each  nut  equal  to  f  of  the  screw  diameter. 
We  recommend  the  latter  method  and  have  used  these  pro- 
portions wherever  jam-nuts  are  shown.  This  method  of 


94 


DRAWING  AND   DESIGNING. 


locking  is  too  cumbersome  to  be   used  on  large-sized  nuts. 
It  is  rarely  employed  on  nuts  over  ij"  in  diameter. 

Spring-washer  Nut-lock. — This  consists  of  a  single  coil 
of  a  steel  spring,  NL,  Fig.  63,  which  keeps  the  nut  A"  from 


FIG.  63. 

slacking  back,  by  its  elasticity,  when  the  tension  on  the  bolt 
is  reduced.  It  is  employed  quite  extensively  in  railway- 
engineering  practice  for  securing  nuts  subjected  to  the  heavy 
vibrations  common  to  this  class  of  work.  The  form  shown 
in  Fig.  63  is  that  made  by  the  American  Brake  Beam  Co., 
and  is  employed  to  secure  the  nuts  on  the  bogie  frames,  etc., 
manufactured  by  them.  In  the  cross-section  the  top  of  the 
washer  is  inclined  ^  of  an  inch,  and  when  the  nut  is  screwed 
home  its  under  side  conforms  to  the  part  of  the  washer  in 
contact  with  it.  The  following  proportions  agree  approxi- 
mately with  the  washers  manufactured  by  the  afore-mentioned 
company: 

The  outside  diameter  =  J?  the  distance  across  the  flats  of 
the  nut  +  Ty. 


SCREWS,  NUTS,  AND   BOLTS.  <,$ 

The  inside  diameter  —  d  the  diameter  of  the  bolt  +  ¥'• 

The  mean  thickness  t  is  equal  to  the  width  w. 

Exercise  18 — Draw  an  elevation  of  a  spring-washer  nut- 
lock  before  the  nut  is  screwed  clown,  as  shown  in  Fig.  63. 
Make  d  =  \"  diameter.  Scale  twice  full  size. 

Wiles's  Nut-lock,  shown  in  Fig.  64,  is  an  ordinary  nut 
sawn  half  way  across.  After  the  nut  is  screwed  home  the 


FIG.  64. 

opening  is  partly  closed  by  the  screw  5,  which  causes  the 
threads  in  the  upper  part  of  the  nut  to  clamp  the  correspond- 
ing threads  of  the  bolt.  The  thickness  t  of  the  clamping 


96 


DRA  WING  AND   DESIGNING. 


part  of  the  nut  may  be  made  equal  to  twice  the  pitch  of  the 

T~*  7 

threads.       The    diameter    of    the    screw    S= ,    where 

2  2 

F=  distance  across  the  flat  sides  of  the  nut,  and  ^/ nominal 
diameter  of  bolt.  As  there  is  not  sufficient  room  on  nuts 
under  i"  in  diameter  to  use  a  set-screw,  they  are  locked  by 
partly  closing  the  saw-cut  with  a  hammer  blow  before  the 
nut  is  put  upon  its  screw. 


UR. 


FIG.  65. 

Nuts  Locked  by  Means  of  Set-screws. — The   arrange- 
ments shown  in   Fig.  65  are  used  on   quick-moving  parts  of 


SCREWS,  NUTS,  AND  BOLTS.  97 

machines.  They  are  neat  in  appearance,  simple,  and  effect- 
ive when  subjected  to  the  worst  conditions.  In  Fig.  65  the 
lower  part  of  the  nut  is  turned  to  form  a  cylindrical  projec- 
tion which  fits  into  a  corresponding  counterbore  in  one  of  the 
pieces  connected  by  the  bolt.  Through  the  latter  passes  a 
set-screw  S,  the  point  of  which  presses  on  the  bottom  of  the 
groove  cut  upon  the  cylindrical  projection,  to  keep  the  burs 
raised  by  the  set-screw  from  interfering  with  the  nut  being 
removed. 

The  follov/ing  proportions-  agree  with  general  practice: 


"  ;  G=  diameter  of  set  screw  at 

5  =  %d  +  £'  ;  the  bottom  of  the  threads  ; 

c  =  2$  =  fc/+i";  A  =  ii</; 

F  =  5;  £==  ii</-4"; 

/  =  d\  r  =  half    the    distance   across 

the  angles  of  the  nut-j-J". 

In  addition  to  the  locking  device  it  is  usual,  on  quick- 
moving  parts,  to  extend  the  bolt  beyond  the  nut.  This 
extension  E,  called  a  pin-point,  has  the  threads  cut  off  and  a 
hole  drilled  through  it  into  which  is  fitted  a  split  pin  SP. 
This  renders  the  nut  secure  against  coming  off,  but  does 
not  necessarily  prevent  its  slacking.  The  diameter  of  the 
split  pin  SP  is  .05^-)-  .13,  /=  2j  times  the  diameter  of  the 
split  pin,  dl  =  diameteY  at  the  bottom  of  the  threads.  A 
method  of  drawing  split  pins  is  shown  in  Fig.  69. 

Exercise  19  —  Draw  a  plan,  front  elevation  and  end  eleva- 
tion of  the  locking  arrangement,  shown  in  Fig.  65,  showing 
the  application  of  the  arrangement  on  a  connecting-rod  end 
of  the  form  shown  in  Fig.  66.  Make  d  =  4$"  '.  Scale  half 
size. 


98  DRA  WING  AND  DESIGNING. 

Construction. — Locate  the  centre  lines,  draw. the  hexagon' 
and  the  part  of  the  connecting-rod  end.  in  plan.  This  is  as 
far  as  we  can  proceed  without  the  elevation.  Draw  the  part 
of  the  connecting-rod  in  front  elevation  and  complete  the 
locking  arrangement,  projecting  the  parts  already  drawn  in 
the  plan  view.  Taking  our  measurements  from  the  plan,  and 
projecting  from  the  front  elevation,  we  can  complete  the  end 
elevation.  We  can*  now  complete  the  plan  from  the  front 
elevation  by  projecting  the  parts  not  already  drawn  in  that 
view.  The  method  of  drawing  the  curve  formed  by  cutting 
the  fillet  to  allow  the  'nut  to  bear  upon  a  flat  surface,  will  be 
understood  by  following  the  construction  lines  I,  2,  3,  4, 
5,  6.  In  drawing  office  practice  this  curve  is  usually  drawn 
by  an  arc  of  a  circle  passing  through  the  limiting  points. 
All  parts  are  dimensioned  in  inches. 

When  it  is  undesirable  to  counterbore  the  piece  upon  which 
the  nut  bears,  as  in  Fig.  6$,  the  cylindrical  portion  of  the  nut 
is  made  to  fit  into  the  collar  C,  Fig.  66,  which  is  carried 
upon  the  outer  surface  of  the  connected  piece,  and  kept  from 
rotating  by  means  of  the  pin  P.  The  nut  is  secured  by  the 
set-screw  5"  passing  through  the  collar  and  pressing  on  the 
bottom  of  the  groove  which  is  cut  upon  the  cylindrical  part 
of  the  nut.  In  some  cases  the  pin  P  is  fitted  into  the  hole 
in  the  connected  piece,  but  in  the  example  shown  in  Fig.  66 
it  is  screwed  into  the  piece  to  avoid  the  risk  of  losing  it  when 
the  nut  and  collar  are  removed.  The  proportions  of  the  nut 
are  the  same  as  in  the  last  exercise.  The  collar  proportions 
are  D  =  2</,  c  =  2S  =  ±d  +  {".  The  diameter  of  P  =  \d 
+  Ty .  The  length  of  P=  2  times  its  diameter,  half  of 
which  fits  into  the  collar. 


,  NUTS,  AND    BOLTS. 


99 


Exercise  20  —  Draw  an  elevation  of  the  locking  arrange- 
ment shown  in  Fig.  66.      Make  d  =  2".      Scale  full  size. 


D.R. 


FIG.  66. 


Circular  Nut-locking  Device. — The  nut  and  its  locking 
arrangement  shown  in  Fig.  67  are  used  for  securing  the 
piston-rod  to  across-head  of  the  form  shown  in  Fig.  67.  On 
the  outer  surface  of  the  nut  N,  longitudinal  grooves  are  cut, 
into  which  the  projections  on  the  spanner,  employed  for 
screwing  it  up,  fit.  The  locking-plate  LP  consists  of  a  plate 
shaped  to  suit  the  curvature  of  the  nut,  and  has  a  projection 
which  fits  into  one  of  the  spanner  grooves.  The  stud  5  is 
screwed  into  the  surface  upon  which  the  nut  is  carried,  pass- 
ing through  the  groove  in  the  locking-plate  (LP)  and  is  pre- 
vented from  unscrewing  by  making  the  part  within  the 


100 


DRAWING   AND  DESIGNING. 


locking-plate  square.      The  method  of  locking  the  nut  is  as 
follows:  The  stud  S  is  screwed  into  the  metal  at  the  proper 


FIG.  67. 

distance  from  the  centre  of  the  nut  TV,' forming  an  angle  with 
the  radial  line  which  passes  through  the  centre  of  the  projec- 


SCREWS,  NUTS,  AND   BOLTS.  IOI 

tion  on  the  'locking-plate  equal  to  half  the  angular  distance 
between  two  of  the  spanner  slots.  This  allows  the  nut  to 
be  locked  in  any  position.  After  the  nut  N  \s  screwed  into 
position,  the  locking-plate  LP,  with  its  projection  fitting  into 
one  of  the  grooves,  is  passed  over  the  stud  until  it  rests  upon 
the  piece  fastened  by  the  nut  N.  The  nut  can  then  be 
locked  securely  by  clamping  the  locking-plate  LP,  by  screw- 
ing down  N.  The  nut  N  has  a  cylindrical  projection  on  the 
under  side  which  fits  into  a  corresponding  recess  in  the  piece 
upon  which  it  bears.  This  insures  that  the  outside  of  the 
nut  is  concentric  with  the  arc  which  passes  through  the 
centre  of  the  locking-plate.  It  also  gives  a  greater  length  of 
nut  without  increasing  the  distance  which  the  nut  projects 
from  the  piece  it  is  fastening. 

The  proportions  of  the  nut  and  its  locking  device  are  as 
follows  : 

D  =  diameter  across  the  angles  of  the  hexagon; 
F  =  diameter  across  the  flats  of  the  hexagon; 


t  =  TV; 

V/=  .04^+.  13. 

Make  the  diameter  d'  of  the  stud  5  =  \"  when  nut  N  is 
2"  or  under,  and  -f"  for  all  nuts  over  2"  in  diameter.  The 
width  of  the  groove^  in  the  locking-plate  equal  to  the  diam- 
eter of  the  stud  +  TV'-  The  width  of  the  square  body  on 
the  stud  =  d'  and  its  length  =  /  —  -J". 

Exercise   21.  —  Draw    a    fluted    circular    nut    and    locking 


102  DRAWING  AND   DESIGNING. 

arrangement,  as  shown   in  Fig.  67.      Make  d  =  6".      Scale  8" 
to  the  foot. 

Construction. — Locate  the  centre  lines,  draw  the  circle 
making  the  diameter  F=  ijdf+i".  Tangent  to  the  circle 
draw  the  line  2  to  make  an  angle  of  30°  with  the  horizontal. 
Determine  the  radius  r  of  the  arc  passing  through  the  centre 
of  the  nut-lock  and  complete  the  plan  of  the  nut-lock. 
Determine  the  centres  of  the  spanner  grooves  by  circumscrib- 
ing on  the  half  of  the  circle  I,  three  sides  of  a  hexagon,  as 
in  Fig,  67.  The  sides  of  the  groove  are  parallel  to  the  radial 
lines  which  bisect  the  angles  formed  by  the  sides  of  the 
hexagon.  Projecting  from  the  plan  complete  the  elevation. 
Construction  lines  are  not  to  be  inked  in. 

In  Fig.  68  is  shown  a  nut-locking  device  used  for  secur- 
ing the  piston-rod  to  the  piston  shown  in  Fig.  66.  The  nut 
N  in  this  case  is  of  cast  steel  and  has  a  projection  on  the 
under  side  which  fits  into  a  corresponding  recess  in  the  lock- 
ing-plate LPj  which  in  turn  fits  into  a  circular  recess  on  the 
piston.  The  locking-plate  has  a  tapped  hole  through  it,  and 
through  this  tapped  hole,  at  right  angles  to  its  axis,  the  ring 
is  cut.  After  the  nut  with  its  locking-plate  has  been  screwed 
into  place  a  tapered  plug  -Pis  inserted  into  the  tapped  hole. 
This  opens  the  saw-cut  and  forces  the  locking-plate  against 
the  sides  of  the  circular  recess  on  the  piston.  The  nut  is 
thus  securely  locked  by  the  friction  caused  by  the  pressure 
of  the  locking-plate  against  the  sides  of  the  recess.  The 
following  proportions  may  be  used  for  the  nut  and  locking- 
plate: 

d  =  nominal  diameter  of  screw; 

F  —  distance  across  the  flats — J"; 


SCREWS,  NUTS,  AND  BOLTS. 


103 


IO4  DRA  WING   AND   DESIGNING. 

t  —  thickness    of   standard   nut  having  the  same  number  of 

threads  per  inch  ; 

H  =  d  +  thickness  of  locking-plate  ; 
T  =  .o9d+  .7. 

The    size    of   the    pipe-tap    is  =  -§-</,  but  need  not  exceed 

f"    pipe-tap.      The    projection    on     the     under    side    of    the 

nut   —  T-}-  ¥y   to  allow  the  nut  to   bear  upon   the  piston. 

W —  twice  the  diameter  of  the  tapped  hole  at  the  small  end. 

Exercise  22 — Draw  the  nut-locking  arrangement  shown 
in  Fig.  68,  showing  part  of  the  piston  and  piston-rod.  Make 
^—  3"  and  having  5  threads  per  inch.  Scale  full  size. 

Construction. — To  find  the  distance  across  the  flats  of  the 
hexagon  turn  to  Table  8,  page  72,  and  find  the  thickness 
of  a  nut  having  5  threads  per  inch  by  subtracting  the  radius 
of  the  screw  from  half  the  distance  across  the  flats.  To  find 
the  diameter  of  the  tapped  hole  at  the  small  end,  turn  to  the 
table  of  Wrought-iron  Pipes  on  page  57-  The  size  of  the 
actual  outside  diameter  is  the  diameter  of  the  tapped  hole  at 
the  large  end,  and  the  hole  is  -fa"  less  in  diameter  for  every 
i"  of  its  length.  Complete  the  drawing,  substituting  the 
dimensions  in  inches  for  the  reference  letters,  and  give  the 
number  of  threads  per  inch  on  the  piston-rod  screw  and  the 
nominal  diameter  of  the  pipe-tap. 

Pin  and  Pin-joints. — Pins  connect  pieces  by  their  resist- 
ance to  shearing  at  one  or  two  cross-sections. 

Split  Pins,  when  made  of  a  uniform  diameter  from  wire 
of  a  semicircular  cross-section  and  provided  with  a  head, 
as  in  Fig.  69,  are  used  for  preventing  pieces  from  sepa- 
rating, while  allowing  a  slight  motion  in  the  direction  of 
the  axis  of  the  piece  that  they  pass  through,  as  in  Fig.  67. 


SCREWS,  NUTS,  AND   BOLTS. 


105 


The  method  of  drawing  split  pins  is  clearly  shown  in  Fig.  69. 
The  diameter  of  the  pin,  in  proportion  to  the  diameter  d  of 


DR. 


FIG. 


the  piece  it  passes  through,  may  be  =  .05^  -f-  •*$»  taking  the 
nearest  size  in  T^". 

Taper  Pins,  shown  in  Fig.  70,  are  used  for  securing  one 
piece  to  another  in  a  fixed  position,  as  shown  in  Fig.  71. 


FIG.  70. 

They  are  sometimes  split  at  the  small  end,  and  opened  out 
in  the  same  manner  as  the  ordinary  split  pin,  to  prevent 
slacking  back.  The  diameter  of  the  tapered  pin  at  the  large 
end,  in  proportion  to  the  diameter  (d)  of  the  piece  through 
which  it  passes,  may  be  made  =  .o6d -\-  .13  and  taking  the 
nearest  size  from  Table  10. 


io6 


DRA  WING  AND   DESIGNING. 
TABLE    10. 

STANDARD    STEEL    TAPER-PINS. 

Taper  one-quarter  inch  to  the  foot. 


3 

4 

5 

7 

9 

10 

Diameter  at     ( 
large  end  | 

.156 

.172 

•  193 

.219 

.250 

.289 

•341 

.409 

.492 

•591 

.706 

Approximate   ) 
fractional  V 
sizes  j 

5/32 

11/64 

3/i6 

7/32 

X 

19/64 

11/32 

13/32 

X 

19/32 

23/32 

Longest  limit  | 
of  length    ) 

I 

iX 

iH 

in 

2 

2X 

3X 

3X 

4^ 

sX 

6 

A  Knuckle-joint  is  a  pin-joint   used  for  connecting  two 
rods  in  such  a  manner  that  one  of  them  will  have  a  rotary 


_    ^£      _  <2 

^f  J      ~ 


D.R. 


FIG.  71. 


FIG.  72. 


motion  in  one  plane.  The  connection  is  made,  as  shown  in 
Fig.  71,  by  the  pin  P  passing  through  the  fork,  or  double 
eye,  formed  on  the  rod  R,  and  the  single  eye,  on  the  rod  R' ', 


SCREWS,  NUTS,  AND   BOLTS. 


107 


which  fits  into  the  fork.  The  parts  of  the  rods  near  the  tve 
and  fork  are  either  left  square  or  have  the  corners  taken  off 
for  a  distance,  which  makes  a  part  of  the  rod  octagonal  in 
cross-section.  In  the  arrangement  shown  in  Fig.  71,  the  pin 
P  is  allowed  to  turn  and  is  kept  in  place  by  the  collar  C, 
which  is  secured  to  the  turning-pin  P  by  driving  a  taper-pin 
through  it  and  the  collar.  The  width  W  of  the  collar  should 
not  be  less  than  2^  times  the  diameter  of  the  taper-pin. 

Another  method  in  common  use  for  holding  the  turning- 
pin  in  place  is  to  use  a  loose  washer  (IV)  and  split  pin,  as 
shown  in  Fig.  72.  In  Fig.  73,  the  pin  P  is  held  against 


D.fi. 


FIG.  73- 

turning  by  a  taper-pin  p  driven  transversely  through  one  of 
the  eyes  on  the  rod  R  and  partly  into  the  pin  P.  By  this 
arrangement  all  the  wear,  due  to  the  turning  motion,  is  on 
the  eye  of  the  rod  R ',  which  is  fitted  with  a  steel  or  bronze 
bush. 


108  DRAWING  AND   DESIGNING. 

The  Proportions  given  in  Figs.  72  and  73  make  the 
joint  stronger  than  the  solid  rod.  This  is  necessary  to  allow 
for  bending  stresses  produced  when  the  pin  becomes  worn. 
Unit  of  proportions  d. 

Exercise  23 — Draw  a  PLAN,  ELEVATION,  and  END  VIEW 
of  the  joint  shown  in  Fig.  71,  showing  the  method  of  holding 
the  pin  in  place  by  means  of  a  split  pin  and  washer.  Make 
d=  \"  Scale  full  size. 

Exercise  24 — Draw  a  PLAN  partly  in  section,  an  ELEVA- 
TION and  SECTIONAL  END  VIEW  (the  plane  of  section  passing 
through  the  rod  at  the  line  ab)  of  the  knuckle  joint  shown  in 
Fig.  73.  Make  d  =  i£".  Scale  full  size. 


CHAPTER    II. 
KEYS,   COTTERS,  AND  GIBS. 

Keys  are  employed  to  connect  wheels,  cranks,  cams, 
etc.,  to  shafting  transmitting  motion  by  rotation.  They  are 
generally  made  of  wrought  iron  or  steel,  and  are  commonly 
rectangular,  square,  or  round  in  cross-section.  The  form  of 
key  in  general  use  is  made  slightly  tapered  and  fits  accurately 
into  the  key-way,  offering  a  frictional  holding  power  against 
the  keyed  piece  moving  along  the  shaft.  The  groove  or  part 
where  the  key  fits  on  the  shaft,  and  the  groove  into  which  it 
fits  on  the  piece  it  is  holding  is  called  the  key-bed,  key- 
way  or  key-seat.  For  square  or  rectangular  keys,  when  the 
keyed  piece  is  stationary  on  the  shaft,  the  .bottom  of  the 
groove  on  the  shaft  is  parallel  to  the  axis,  while  that  of  the 
groove  in  the  piece  it  is  securing  is  deeper  at  the  one  end 
than  the  other  to  accommodate  the  taper  of  the  key. 

Keys  may  be  divided  into  three  classes:  I.  Concave  or 
saddle  key;  2.  flat  key;  3.  sunk  key. 

Saddle  Key. — This  form  of  key  has  parallel  sides,  but  is 
slightly  tapered  in  thickness  and  is  concaved  on  the  under 
side  to  suit  the  shaft,  as  shown  in  Fig.  74.  As  the  holding 
power  depends  entirely  upon  the  frictional  resistance,  due  to 
the  pressure  of  the  key  on  the  shaft,  the  saddle  key  is  only 

109 


no 


DRA  WING   AND   DESIGNING. 


adapted  for  securing  pieces  subjected  to  a  light  strain.  When 
this  key  is  used  for  securing  a  piece  permanently,  the  taper  is 
usually  made  I  in  96,  but  when  employed  on  a  piece  requir- 
ing to  be  adjusted,  such  as  an  eccentric,  the  taper  is  increased 
to  I  in  64  to  allow  the  key  to  be  more  easily  loosened. 


FIG.  74- 


FIG.  75- 


Flat  Key. — This  form  of  key,  Fig.  75,  differs  from  the 
saddle  key  in  that  it  rests  on  a  flat  surface  filed  upon  the 
shaft.  It  makes  a  fairly  efficient  fastening,  but  as  it  drives 
by  resisting  the  turning  of  the  shaft  under  it,  there  is  a  tend- 
ency to  burst  the  keyed-on  piece. 


TABLE   11. 

DIMENSIONS    OF    SADDLE   AND    FLAT    KEYS. 


D 
B 

T 


5/i6 


3/16 


7/16 


# 

5/i6 


3 
5/i6 


5 
7/16 


7 
9/16 


Sunk  Keys  are  so  called  because  they  are  sunk  into  the 
shaft  and  the  keyed-on  piece,  Fig.  76,  which  entirely  pre- 
sents slipping.  For  engine  construction  they  are  usually 
rectangular  in  cross-section  and  made  to  fit  the  key-seat  on 
all  sides.  When  subjected  to  strains  suddenly  applied,  and 


KEYS,   COTTERS,  AND    GIBS. 


Ill 


FIG.  76. 

in    one    direction,    they    are    placed    to    drive    as    a    strut, 
diagonally,  as  in  Fig.  77. 


D.P. 


FIG.  77. 


FIG.  78. 


The   following  table,   taken   from    Richards's   "  Machine 
Construction,"  agrees  approximately  with  average  practice: 


TABLE   12. 

DIMENSIONS    OF    RECTANGULAR   SUNK    KEYS. 


D 

B 
T 


i 
5/32 


5/i6 


7/16 

9/32 


2 

5/i6 


3 

7/16 


5 
iJ/16 


6 
13/16 


In    mill-work,    for   fastening   pulleys,    gear-wheels,    coup- 
lings, etc.,  to  shafting  they  are  made  slightly  greater  in  depth 


112 


DRAWING   AND    DESIGNING. 


than  breadth.  For  machine  tools  they  are  generally  square 
in  cross-section.  The  following  table  gives  the  sizes  of  keys 
used  by  Wm.  Sellers  &  Co.  both  for  shafting  and  machine 

tools: 

TABLE   13. 


D 

i* 

3i 

2 

2X 

*j 

^ 

3 

3X 

& 

B 

5/i6 

5/i6 

7/16 

7/16 

9/16 

11/16 

Il/lfi 

11/16 

11/16 

T 

/2 

rs 

K 

^ 

K 

M 

D 

4 

4K 

5 

5# 

6 

6K 

7 

7^ 

8 

B 

13/16 

13/16 

13/16 

15/16 

15  '16 

15/16 

iyV 

iTV 

T 

% 

7/8 

H 

i 

i 

i 

1/8 

m 

1/8 

Round  Keys. — Taper-pins  (Fig.  78)  are  sometimes  used 
as  keys  to  prevent  rotation  where  a  crank  or  wheel  is  shrunk 
on  to  the  end  of  a  shaft  or  axle.  Round  keys  are  used  in 
such  a  case  because  of  the  ease  in  forming  the  key-way, 
which  is  simply  a  tapered  round  hole  drilled  half  into  the 
shaft  and  half  into  the  shrunk-on  piece.  The  standard  pro- 
portions of  the  pins  are  given  on  page  106.  The  size  at  the 
large  end  nearest  to  J  of  the  shaft  diameter  may  be  used  for 
this  purpose. 

Fixed  Keys  are  used  when  it  is  undesirable  to  cut  a  long 
key-way  on  the  shaft  to  allow  the  key  to  be  driven  into  place 
after  the  keyed-on  piece  is  in  position.  The  fixed  key  is 
sunk  into  the  shaft,  as  in  Fig.  79,  and  the  keyed-on  piece  is 
driven  into  position  after  the  key  is  in  place, 

When  a  keyed-on  piece  has  to  be  adjusted  to  different 
positions  on  the  shaft,  to  avoid  the  trouble  of  drawing  a 
tight  key  in  and  out,  it  is  made  to  slide  in  the  key-way,  and 
the  keyed-on  piece  is  held  against  moving  along  the  shaft  by 
means  of  set-screws,  as  shown  in  Fig.  80. 


KEYS,   COTTERS,  AND    GIBS. 


FIG.  79.  FIG.  So. 

Sliding  Feather  Key. — This  system  of  keying  secures 
the  piece  to  the  shaft,  to  transmit  motion  of  rotation,  and  at 
the  same  time  allows  the  keyed-on  piece  to  move  along  the 


DP. 


FIG.  81.  FIG.  82. 

shaft.  They  may  be  secured  to  the  keyed  piece  and  slide  in 
a  groove  on  the  shaft,  as  in  Fig.  81,  or  secured  to  the  shaft 
and  slide  in  the  groove  in  the  keyed  piece,  as  in  Fig.  79. 
The  dimensions  for  this  form  of  key  may  be  taken  from 
Table  13. 

Woodruff  Keys. — This  system  of  keying  (Fig.  %2a)  is 
used  for  machine  tools,  or  wherever  accurate  work  is  of  first 
importance.  With  this  form  of  key,  as  the  key  rights  itself 
to  the  groove  in  the  keyed-on  piece,  there  is  no  danger  of 


114  DRAWING   AND   DESIGNING. 

the  work  being  thrown  out  of  true  by  badly  fitted  keys,  and, 
being  deep  in  the  shaft,  it  cannot  turn  in  the  key-seat. 


FIG.  %2a. 

Key-heads- — When  the  point  of  a  key  cannot  be  con- 
veniently reached  for  the  purpose  of  driving  it  out,  a  head  is 
formed  on  one  end,  as  shown  in  Fig.  76.  Which  shows  the 
proportions  and  method  of  construction  given  in  RlCHARDS'S 
"MACHINE  CONSTRUCTION." 

Strength  of  Keys. — The  driving  power  of  saddle  keys 
or  keys  on  flats  cannot  be  calculated  with  any  degree  of 
accuracy.  They  are  used  only  where  the  power  transmitted 
by  the  keyed  on  piece  is  small. 

Sunk  Keys  are  subjected  to  shearing  and  crushing 
strains,  and  are  required  (i)  to  transmit  the  whole  of  the 
power  transmitted  by  the  shaft,  as  in  crank-shaft  couplings, 
etc.,  or  (2)  only  a  part  of  the  power  transmitted  by  the 
shaft,  as  when  fastening  pulleys,  eccentrics,  etc.  As  a 
general  rule,  however,  all  keys  are  proportioned  to  suit  the 
first  conditions,  unless  where  the  amount  of  power  trans- 
mitted by  the  shaft  is  exceedingly  great  in  comparison  with 
that  taken  off  at  the  keyed-on  piece. 

Let  B  —  breadth  of  key; 
L  =  length  of  key; 

—  =  radius  at  which  key  offers  a  resistance; 


KEYS,   COTTERS,  AND    GIBS.  11$ 

the   shearing  of    the  material  which    is  =  9000 

for  wrought  iron  and  11,000  for  steel. 

.igod*fs  =  modulus  of  the  section  of  shaft  for  torsion 
=  \j2Ocr  for  wrought-iron  and  2182^*  for 
steel  shafts; 

R  =  the  radius  of  arm  through  which  P,  the  power, 
is  transmitted. 

Under  the  first  conditions  the   strength  of  a  tight  key 
would  be  found  by  the  formula 


.....     (16) 


and  under  the  second  conditions  by  the  formula 


f,BLd-  =  PR  .......     .     (17} 


In  the  system  of  sliding  keys  the  crushing  action  on  the 
key  is  greater  than  when  the  key  is  a  tight  fit  in  the  key-way, 
and  keys  of  this  type  should  be  proportioned  to  have  the 
moment  of  shaft  torsion  =  the  moment  of  key  shearing  = 
moment  of  key  crushing.  Then 


-=fc>      ...     (18) 


and  if  we  take/,  =  2fs  ,  then  T  =  B.      In  practice,  however, 
B  is  generally  greater  than  T. 

Length  of  Key.  —  From  the  foregoing  formulae  it  will  be 
seen  that  the  strength  of  the  key  is  directly  proportional  to> 
(L)  the  length.  To  find  the  length  L  when  the  full  power  of 


Il6  DRAWING   AND   DESIGNING. 

the    shaft    is    to    be    transmitted    through   the    key.      From 
formula  No.  17 


i  \oooBL-  =  2i82</°, 
21824" 


substituting  the  value  of  B  from  Table  12  in  terms  of  d 

2182^' 


Hence  when  the  shaft  and  the  key  are  of  the  same  material, 
the  length  (L)  of  the  common  key  (Table  12)  should  not 
be  less  than  i.6d.  When  the  hub  of  the  keyed-on  piece  is 
so  short  that  one  key  has  not  sufficient  strength,  two  or  more 
keys  are  used.  Where  two  keys  are  used  they  should  be 
placed  at  right  angles  to  each  other.  By  this  arrangement  the 
keyed-on  piece  is  held  upon  three  points,  which  prevents  it 
from  rocking  upon  the  shaft  when  the  shaft  is  not  a  tight  fit 
in  the  hole. 

COTTERS 

are  keys  employed  to  connect  pieces  which  are  subjected 
to  tensile  and  compressive  forces.  They  are  driven  trans- 
versely through  one  or  both  of  the  connected  pieces  and 
transmit  power  by  a  resistance  to  shearing  at  two  cross- 
sections.  The  cotters  are  usually  made  rectangular  in  cross- 
section,  and  the  ends  rounded,  as  shown  in  Fig.  83. 

The    cotter-way    with    the    rounding    ends    is    generally 
adopted,  as  it  is  easier  to  make,  which  is  done  by  drilling  two 


KEYS,   COTTERS,  AND    GIBS.  117 

holes  of  a  diameter  equal  to  the  thickness  of  the  cotter  and 
cutting  out  the  metal  between  them.  Again,  this  form  of 
cotter-way  does  not  weaken  the  cottered  pieces  to  quite  the 
same  extent  as  when  the  corners  are  left  sharp.  The  cotters, 
however,  are  not  so  easily  fitted  into  cotter-ways  with  round 
ends,  and  for  that  reason  some  engineers  make  the  cotters  of 
rectangular  cross-section,  fitted  into  corresponding  cotter- 
ways. 


J 

1- 

-L 

T 

i 

_.u... 

i 

^x 

I— 

s     T 

i     . 

^ 

DM. 


FIG.  83. 


Taper  of  Cotters. — When  cotters  are  employed  as  a 
means  of  adjusting  the  length  of  the  connected  pieces,  or  for 
drawing  them  together,  they  are  made  tapered  in  width,  as 
in  Fig.  83,  but  when  used  as  a  holding-piece  only,  the  sides 
are  parallel,  as  in  Fig.  56.  When  tapered  cotters  depend 
upon  the  friction  between  their  bearing-surfaces  for  retaining 


Il8  DRAWING   AND    DESIGNING. 

them  in  position  the  taper  should  not  be  more  than  I  in  24 
(J"  per  foot),  but  where  special  means  are  employed  for 
holding  the  cotter  against  slacking,  the  taper  may  be  made 
as  great  as  I  in  6  (2"  per  foot). 

Forms  and  Proportions  of  Cotter-joints. — When  the 
fastening  is  subjected  to  tension  only,  the  arrangement 
shown  in  Fig.  84  is  used  for  securing  two  pieces  together  by 
means  of  a  cotter.  Fig.  83  shows  a  method  of  fastening  two 
rods,  R  and  R\  together  to  resist  thrust  and  tension.  The 
joint  is  made  by  fitting  the  end  of  the  rod  R  into  a  socket  6* 
formed  on  the  end  of  the  rod  R',  and  through  the  socket  and 
rod  end  driving  a  cotter  until  the  collar  C  bears  against  the 
socket  end. 

As  a  cotter-joint  is  proportioned  to  withstand  the  greatest 
longitudinal  force  transmitted  by  the  rod,  all  parts  will  there- 
fore be  proportional  to  the  diameter  d^  of  the  rod,  unless 
where  the  dimensions  of  the  rod  are  increased  to  insure  stiff- 
ness. The  following  proportions  are  in  accordance  with  good 
practice: 

b,  breadth  of  cotter  =  1.3^,; 

/,  thickness  of  cotter  =  .3^,; 

d,  diameter  of  pierced  rod  =  1.2^; 

D,  diameter  of  socket  in  front  of  cotter  =  2.4^,  or  2d. 

D, ,  diameter  of  socket  behind  cotter  =  2^,; 

/}, ,  diameter  of  collar  on  rod  R  —  1.5^,; 

t,  thickness  of  collar  on  rod  R  =  J^; 

/,  the  length  of  the  rod  and  socket  beyond  the  cotter  =  from 

K  to  4. 


KEYS,   COTTERS,  AND    GIBS. 


119 


When  d  is  known  the  diameter  of  the  solid  rod  (V,)  = 
The  clearance  c  may  be  made  -J-".  The  cotter  need 
not  extend  beyond  the  greatest  diameter  of  the  socket  more 
than  4"  when  driven  home. 

Fig.  84  shows  an  arrangement  often  used  for  securing  an 
engine  piston-rod  to  the  piston.  Here,  instead  of  having  a 
collar  on  the  rod  R  to  resist  the  thrust,  the  rod-end  is 
tapered. 


FIG.  84.  FIG.  85. 

In  Fig.  85,  the  pierced  part  of  the  rod  has  a  smaller 
diameter  than  the  solid  rod.  Such  a  condition  is  possible 
when  the  diameter  of  the  rod  is  increased  in  consequence  of 
its  having  to  resist  buckling  stresses.  The  joint  being  sub- 
jected only  to  tension  and  compression,  the  rod  would  under 
these  conditions  be  excessively  strong  if  proportioned  to  the 
diameter  of  the  solid  rod.  We  must  therefore  find  the 
diameter  (*/,)  and  proportion  the  joint  independently  of  the 
actual  rod  diameter,  d^  is  found  by  the  formula — 


from  which 


(19) 


•78547, 

Where  P  is  the  pull   on  the  rod.  ^For  steel  rods  ft  may  be 
taken  at  7000  and  5000  for  wrought  iron.     The  taper  of  the 


120  DRAWING   AND    DESIGNING. 

rod-end  may  be  made  from  J"  to  i"  per  foot  of  length,  i.e., 
from  i  in  12  to  I  in  24.  The  diameter  d  on  the  tapered  rod- 
end  is  taken,  when  the  cotter-way  is  curved  at  the  end, 
where  the  curve  begins,  as  in  Fig.  84,  and  at  the  end  of  the 
cotter-way  when  the  cotter-way  is  rectangular. 

Exercise  25 — Draw  a  SECTIONAL  ELEVATION,  a  HALF 
PLAN,  and  HALF  SECTIONAL  PLAN  of  the  cotter-joint  shown 
in  Fig.  83.  Make  d=  2".  Scale  f till  size. 

Exercise  26 — Design  cotter-joints  suitable  for  fastening  a 
steel  piston-rod  to  the  piston  and  cross-head,  as  shown  in 
Figs.  84  and  85.  Make  the  diameter  of  the  rod  d^  =  2f"  and 
assume  that  the  rod  is  subjected  to  a  load  of  9000  Ibs.  The 
rod-ends  having  a  taper  of  I  in  12.  Scale  full  size. 

Construction. — Having  determined  the  diameter  (d)  of  a 
rod  suitable  for  resisting  tensile  stresses,  then  from  d  find  the 
other  proportions  of  the  joints,  as  in  Exercise  25.  Measure 
off  the  distances  /  and  b  along  the  centre  line  and  mark  off  the 
diameter  (d)  at  the  proper  point  according  to  the  shape  of 
the  cotter  in  cross-section,  then  in  the  manner  given  in  the 
construction  in  connection  with  Exercise  13  draw  the  rod- 
end  to  the  given  taper.  The  construction  for  finding 
the  taper  need  not  be  inked  in.  Complete  the  drawing, 
filling  in  the  actual  dimensions  and  leaving  off  all  reference 
letters. 

COTTER   AND    GIB. 

When  one  of  the  pieces  connected  by  the  cotter  is 
a  thin  strap,  as  in  Fig.  86,  a  second  cotter,  called  a 
gib,  is  used.  The  gib  is  provided  with  a  head  at  the 
ends  which  project  over  the  strap  S,  thus  preventing  it 


KEYS,   COTTERS,  AND    GIBS. 


121 


(tne  strap)  from  being  forced  open  by  the  friction  between  it 
and  the  cotter  as  the  latter  is  driven  into  place.  Figs.  86 
and  89  show  the  application  of  gib  and  cotter  to  strap-end 
connecting-rods,  where  R  is  the  rod  and  5  the  strap.  When 
two  gibs  are  used,  as  in  Fig.  88,  the  sliding  surface  on  each 
side  of  the  cotter  is  the  same.  Instead  of  having  both  gibs 
tapered,  as  shown  in  Fig.  88,  one  of  them  may  be  parallel 
and  the  taper  all  on  one  side  of  the  cotter.  The  strength  of 
the  gib  and  cotter  in  combination  is  made  the  same  as  the 


DM. 


FIG.  86. 


FIG.  87. 


FIG.  88. 


single  cotter  and  should  be  proportional  to  the  strap  5.  The 
working  strength  of  the  strap  at  the  thinnest  part  is  found  by 
the  equation 


2BTft  =  P. 


from  which  T=-     -  r (2°) 

where  Pis  the  maximum  pull  on  the  rod,  T  the  thickness, 


122  DRAWING   AND    DESIGNING. 


and  B  the  breadth  of  the  strap.  Then  as  the  gib  and  cotter 
are  to  have  the  same  strength  as  the  single  cotter,  and  as  B 
is  equal  to,  or  a  little  greater  than  d  (the  diameter  of  the  rod). 
/  may  be  made  equal  to  .2^B  and 


T ',  the  thickness  of  the  strap  where  it  is  pierced  by  the  cotter, 
should  not  be  less  than  i.$T.  /',  the  distance  from  the  gib 
to  the  end  of  the  strap,  =  2  T.  /,  the  distance  from  the 
cotter  to  the  end  of  the  rod,  =  1.52".  c,  the  clearance,  should 
not  be  less  than  c'  (the  difference  between  the  widest  part  of 
the  cotter  and  the  width  of  the  cotter  at  the  top  of  the  gib- 
head).  The  method  of  constructing  gib-heads  is  shown  in 
Fig.  87,  where  //,  the  height  of  the  gib-head,  =  ij/. 

Cotter-locking  Arrangements. — A  simple  method,  and 
one  that  is  used  in  nearly  all  cases,  where  possible,  is  to 
screw  one  or  two  set-screws  through  the  rod  until  the  point 
or  points  press  against  the  cotter.  To  keep  the  burs,  raised 
by  the  point  of  the  screw,  from  interfering  with  the  motion 
of  the  cotter,  the  set-screw  bears  on  the  bottom  of  a  shallow 
groove  cut  on  the  side  of  the  cotter,  as  shown  in  Fig.  89. 
The  diameter  of  the  set-screw  need  not  exceed  f".  The 
length  of  the  groove  is  equal  to  the  travel  of  the  cotter 
+  the  diameter  of  the  set-screw.  The  travel  of  the  cotter  is 
the  distance  from  the  top  of  the  gib  (or  where  no  gib  is  used, 
from  the  top  of  the  piece  into  which  the  cotter  passes)  to  the 
top  of  the  cotter  when  the  cotter  is  just  in  place. 

The  width  of  the  groove  is  equal  to  the  diameter  of  the 
set-screw  point,  and  the  depth  =  -fa". 


KEYS,   COTTERS,  AND    GIBS. 


123 


In  Fig.  90  the  cotter  is  locked  by  an  upper  and  lower  nut 
upon  a  screwed  extension  of  the  gib,  which  passes  through  a 
head  formed  on  the  cotter.  This  arrangement  is  used  for 
fastening  in,  and  may  be  used  for  forcing  the  cotter  into, 
oosition. 

d,  the  diameter  of  the  screw  =  /; 
h,  the  height  of  the  head  =  i^d. 

As  the  axis  of  the  locking-screw  is  not  parallel  with  the 
side  of  the  cotter  that  is  in  contact  with  the  gib,  the  hole  in 
the  cotter  head  through  which  the  screw  passes  is  elongated 


D.D. 


FIG.  89. 


FIG.  90. 


to  an  amount  equal  to  the  taper  of  the  cotter  in  its  length  of 
travel  -4-  Ty  for  clearance. 

Exercise  27. — Draw  a  SECTIONAL  ELEVATION  and  a  HALF 

SECTIONAL  PLAN,  a  PLAN,  and  SECTIONAL  END  VIEW  of  a  gib- 
and  cotter-joint  to  resist  a  tension  of  12.000  Ibs.  Make  the 
diameter  (d)  of  the  rod  =  2" .  The  cotter  to  have  an  adjust- 


124  DRAWING   AND    DESIGNING. 

ment   of  .£"  with   a  taper  =   i    in    8.      Show  the   method   of 
locking  the  cotter  by  means  of  a  set-screw.      Scale  full  size. 

Exercise  28. — Draw  a  SECTIONAL  ELEVATION  AND  PLAN 
of  a  double  gib-  and  cotter-joint  as  shown  in  Fig.  88,  with 
the  locking  arrangement  shown  in  Fig.  90.  The  joint  to  be 
proportioned  to  resist  a  tension  of  33,000  Ibs.,  the  cotter  to 
have  an  adjustment  of  f"  and  a  taper  of  I  in  10.  Take  the 
diameter  of  the  rod  —  3".  Scale  full  size. 


CHAPTER    III. 
RIVETS  AND  RIVETED  JOINTS. 

RIVETS  are  made  from  round  bars  of  steel,  wrought  iron, 
copper,  or  brass,  and  are  used  to  fasten  two  or  more  plates 
permanently  together. 

The  plates  to  be  riveted  are  either  drilled  or  punched  with 
holes  -^g-"  larger  in  diameter  than  that  of  the  rivet-shank. 

When  the  rivet  is  placed  in  position  through  the  plates 
a  sufficient  length  of  shank  projects  beyond  the  plates  to  pro- 
vide for  forming  the  rivet-point  head  either  by  hammering  or 
by  machine-pressure  (see  Fig.  92).  Unwin  calls  a  riveted 
joint  the  "  simplest  permanent  fastening." 

Rivets  are  made  by  being  pressed  into  shape  while  red-hot 
with  rivet-making  machines  using  dies  of  suitable  size  and 
form. 

The  names  and  proportions  of  rivet-heads  shown  by  Figs. 
92  to  96  will  be  given  later. 

The  end  of  the  rivet  opposite  to  the  head  before  riveting 
up  is  called  the  point  and  after  riveting  the  point-head. 

Just  before  using  the  rivet  is  heated  red-hot  and  when 
placed  in  position  for  hand-riveting  is  held  there  by  means  of 
a  large  hammer  with  a  long  handle  fulcrumed  at  a  convenient 
distance  from  the  rivet  and  a  man's  weight  applied  at  the  end, 
while  the  point-head  is  made  by  two  riveters  either  in  the  form 
of  the  steeple  head  by  hammers  only  or  the  snap  head  (Fig. 
92)  by  using  a  cup-shaped  die  called  a  snap. 

125 


126  DRAWING   AND    DESIGNING. 

In  machine-riveting  the  point-head  is  pressed  into  shape 
by  suitable  dies,  the  motive  power  being  either  a  lever,  steam, 
hydraulic,  or  pneumatic  pressure.  Machine-riveting  upsets 
the  rivet  and  fills  the  hole  much  better  than  hand-riveting,  be- 
cause the  steady  even  pressure  of  the  former  is  exerted  uni- 
formly through  the  whole  of  the  rivet. 

Hydraulic  riveting  is  preferred  to  steam-riveting,  because 
the  pressure  from  the  former  can  be  gradually  applied,  while 
the  force  from  the  latter  generally  comes  upon  the  rivet  with 
such  rapid  blows  that  sufficient  time  is  not  allowed  for  the 
rivet  to  properly  fill  the  hole. 

Rivet-holes  punched  through  rigid  steel  plates  should 
always  be  annealed  after  punching,  because  the  punching  in- 
jures the  material  surrounding  the  hole  to  such  a  dangerous 
extent  that  the  elasticity  of  the  plate  is  destroyed,  and  when 
the  joint  is  subjected  to  strain  the  stress  is  not  uniformly  dis- 
tributed between  the  rivet-holes.  Another  difficulty  with 
punched  holes  is  the  imperfect  spacing  of  the  rivet-holes. 

Drilled  holes  are  usually  more  expensive  than  punched 
holes  and  the  sharp  square  edge  is  not  as  favorable  to  the  re- 
sistance of  the  rivet  to  shearing,  but  they  are  more  accurate  in 
size  and  spacing,  and  the  resistance  of  the  rivet  to  shearing 
can  be  increased  by  slightly  rounding  the  edges  of  the  holes. 

Calking. — No  riveted  joint  is  ever  perfectly  steam-tight 
without  calking.  This  is  a  process  by  which  a  narrow  strip 
of  the  bevelled  edge  of  one  plate  is  brought  into  forcible 
contact  with  he  plate  beneath  it. 

At  a,  Fig.  91,  is  shown  the  calking-tool  commonly  used 
in  hand-calking,  and  at  b  an  improved  form  of  calking-tool 
patented  bv  Mr.  J.  W.  Connery  of  Philadelphia  and  known  as 


RIVETS  AND    RIVETED  JOINTS. 


127 


the  concave  calking-tool  from  the  concave  finish  aven  to  the 
calked  edge  of  the  plate.  This  is  a  favorite  style  of  calking 
with  locomotive-builders  for  high-pressure  boilers. 


FIG.  91. 

Calking  with  pneumatic  calking-hammers  has  become 
quite  general  in  most  first-class  boiler-shops.  Peabody  and 
Miller  in  their  "Steam-boilers"  describe  a  pneumatic  caik- 
ing-machine  as  follows: 

"  In  general  principle  it  resembles  a  rock-drill  and  consists 
of  a  cylinder  in  which  works  a  piston  and  rod  on  the  end  of 


128  DRAWING   AND    DESIGNING. 

which  is  the  calking-tool.  Air  is  supplied  for  working  the 
piston  at  a  pressure  of  50  or  60  Ibs.  through  a  flexible  tube. 
It  makes  about  1500  working  strokes  a  minute  -^g-"  long.  The 
calker  which  is  about  2\"  in  diameter  outside  and  15"  long 
over  all,  is  held  by  a  workman  who  presses  it  slowtly  along  the 
seam  to  be  calked.  The  edge  of  the  tool  is  well  rounded,  so 
as  not  to  injure  the  lower  plate.  Work  can  be  done  four  times 
as  rapidly  with  the  pneumatic  calker  as  by  hand." 

The  edges  of  rivet-heads  are  not  calked  except  when  they 
show  a  leak  during  the  process  of  testing.  In  some  of  the 
largest  boiler-shops  an  inspector  is  employed  part  of  whose 
duty  it  is  when  examining  a  boiler  to  discover  if  any  of  the 
rivets  are  loose.  This  is  done  by  placing  a  finger  on  the  under 
side  of  the  suspected  rivet  and  tapping  the  top  of  it  with  a 
small  hammer  made  for  the  purpose ;  if  the  rivet  is  not  per- 
fectly tight  it  will  be  easily  detected  by  the  finger;  in  such  a 
case  the  loose  rivet  is  cut  out  and  replaced  by  a  new  one. 

The  Forms  of  Rivets. — The, standard  forms  of  rivets 
in  general  use  are:  (i)  the  button  head  (Fig.  92);  (2)  the 


FIG.  92. 


RIVETS  AND    RIVETED  JOINTS. 


I29 


conical  head  (Fig.  93);  (3)  the  steeple  head  (b}  (Fig.  94); 
(4)  the  steeple  head  (d°)  (Fig.  95);  (5)  the  countersunk  head 
(Fig.  96). 

The  button  head,  or,  as  it  is  sometimes  named,  the  snap 
head,  is  usually  made  with  a  machine-riveter. 

The  conical 'is  also  a  machine-formed  head  and  is  commonly 
used  with  a  button  point-head  or  tail  and  sometimes  with  a 

steeple  point. 

i 

-175 


FIG.  94. 


130 


DRA  WING   AND    DESIGNING? 


The  steeple  point-head  is  the  form  mostly  used  in  hand- 
riveting. 

The  countersunk  point-head  is  only  used  when  there  is  not 
sufficient  room  for  one  of  the  other  forms  and  should  never  be 
used  unless  it  is  impossible  to  avoid  it.  It  is  more  costly 
than,  and  not  as  strong  as,  the  other  forms. 


FIG.  95.  FIG.  96. 

Proportions  of  Rivet-heads. — The  proportions  given  in 
the  figures  in  terms  of  the  diameter  d  are  those  used  by 
the  Champion  Rivet  Co.  and  agree  closely  with  general 
practice. 

Length  of  Rivet-shank. 
The  length  L  (Fig.  92)  for  countersunk  point-head 

and  2  plates id 

For  countersunk  point-head  and  3  plates. id -|— \'f 

For  steeple  point-head 

For  steeple  point-head,  large,  machine-driven 

For  button  point-head 

The  above  proportions  are  good  for  ordinary  boiler-plates, 
but,  since  the  holes  are  -£-$"  larger  than  the   rivet,  the  shank 


RIVETS   AND    RIVETED  JOINTS.  13! 

should  be  increased  in  length  for  thick  plates  to  properly  fill 
the  additional  annular  space. 

The  rivet-shank  is  usually  about  -£-$"  smaller  in  diameter 
than  the  hole  and  has  a  slight  taper  toward  the  point. 

Exercise  29. — Make  a  drawing  of  each  style  of  riveting 
shown  in  Figs.  92  to  96,  making  /  equal  to  J"  and  selecting 
from  Table  14,  page  135,  the  diameter  of  rivet.  For  con- 
ventions see  page  22.  Scale  full  size. 

Riveted  Joints. — There  are  in  common  use  at  least  five 
different  styles  of  riveted  joints,  viz.  :  the  single-riveted  lap- 
joint  (Fig.  97);  the  double-riveted  lap-joint  with  staggered 
spacing  (Fig.  98) ;  the  double-riveted  lap-joint  with  chain 
spacing  (Fig.  99);  the  single-riveted  butt-joint  with  chain 
spacing  (Fig.  100);  the  double-riveted  butt-joint;  the  mul- 
tiple-riveted lap-joint  which  has  more  than  two  rows  of  rivets 
in  the  lap ;  the  multiple-riveted  butt-joint  which  has  more 
than  two  rows  of  rivets  on  each  side  of  the  line  where  the 
plates  butt  together  (Fig.  103). 

NOTATION. 

d  =  the  diameter  of  the  rivet-hole  or  of  rivet  when  riveted 
up. 

p  =  the  pitch  of  the  rivets,  i.e.,  the  distance  from  the  cen- 
tre of  one  rivet  to  the  centre  of  the  next  in  the  same 
row  (Fig.  97).  y 

/  —  the  distance  from  the  centfe  of  rivet-hole  to   edge  of 

plate  (Fig.  97). 
r  =  the  distance  between  the  rows  on  double-riveted  joints. 

rl  =  the  distance  between  outside  rows  of  rivets  on  lap- 
joints  with  welt-strip  and  butt-joints. 


132  DRAWING   AND    DESIGNING. 

m  =  the  least  distance  between  the  edge  of  rivet-hole  and 

edge  of  plate  —  margin  (Figs.  97  to  103). 
/  =  the  thickness  of  plate. 

/t  —  thickness  of  outside  welt-strips  for  butt-joint. 
/,  =  thickness  of  inside  welt-strips  for  butt-joint. 
f  =  thickness  of  inside  welt-strips  for  lap-joint. 
ft  =  the  tensile  strength  per  square  inch  of  the  plate  in  Ibs. 
fs  =  the  shearing  strength  per  square   inch  of  the   rivet    in 

Ibs. 
fff  =  the  shearing  strength  per  square  inch  of  the  plate  in 

Ibs. 
fc  —  the  compressive  or  crushing  strength  per  square  inch  of 

the  plate  in  Ibs. 
R  =  the  radius  of  boiler  in  inches  on  the  outside  of  course 

of  smallest  diameter. 
N  =  the  width  of  widest  welt-strip. 
K  =  the  width  of  narrowest  welt-strip. 
P  =  working  pressure  in  Ibs.  per  square  inch. 
/>—  outside  diameter  of  boiler-shell    at  course   of  smallest 

diameter. 

F  =  factor  of  safety. 
E  =  efficiency  of  riveted  joint. 
T  =  total  tensile  stress. 
a  =  area  of  rivet-hole  =  .7854^** 

Strength  of  Single-riveted  Joint — There  are  five  differ- 
ent ways  in  which  a  single-riveted  lap-joint  may  give  way : 

(1)  Shearing  the  rivet,  as  shown  at  I  in  Fig.  91. 

(2)  Tearing  plate  along  the  centre  line  of  rivets,  shown  at 
2,  2. 

(3)  Tearing  the  plate  through  the  margin,  shown  at  3. 


RIVETS  AND   RIVETED  JOINTS.  ^3 

(4)  Crushing  the  rivet  or  the  plate  in  front  of  the  rivet 

(4,  4). 

(5)  Shearing  the  plate  in  front  of  the  rivet  (5,  5). 
The  shearing  strength  of  the  rivet 

7i  d* 
= X  /,  =  a  X  38,000.        .   ;...     .        (i) 

The  resistance  of  plate  to  tearing  on  centre  line  of  rivet 

=  (P-  d)tXft.       .      .      2     .      .     .        (2) 

The  resistance  of  the  plate  to  tearing  at  3  has  been 
found  by  experiment  to  be  great  enough  when  the  distance 
/is  made  equal  to  i\d,  and,  as  this  rule  agrees  with  general 
practice,  it  will  be  maintained  throughout  this  work. 

The  compressive  resistance  of  the  plate  at  4  is 

t  X  d  X  fc .       (3) 

The  resistance  to  shearing  the  plate  in  front  of  the  rivet 
as  shown  at  5,  5, 

=  2t  x  /  x  /; (4) 

But  if  the  joint  is  made  strong  enough  to  resist  shearing 
the  rivet  or  tearing  the  margin  it  w.ill  be  strong  enough  to 
resist  shearing  or  crushing  the  plate  in  front  of  the  rivet,  so 
that  the  latter  may  generally  be  disregarded. 

The  thickness  of  the  boiler-plate  is 

=  PXKX_F  =     PR 

ft  XE        "  n,oooE'       •     •     •       (5) 


The  value  for  /  should  be  taken  as  the  nearest  even  six- 
teenths of  an  inch.     Take  E  =  .70. 


134  DRAWING   AND    DESIGNING. 

The  thickness  of  dome-sheet  may  be  calculated  by  the 
same  formula. 

In  locomotive-boilers  the  thickness  of  tube-sheets  for  f " 
shells  and  over  should  be  J"  to  -fa" . 

When  shells  are  less  than  f"  thick  it  is  usual  to  make  the 
thickness  of  tube-sheets  equal  to  /  +  •§•". 

The  throat-sheet  is  usually  made  -J-"  thicker  than  the 
shell  to  allow  for  extra  flanging. 

In  thick  shells,  fr/  or  over,  Ty  thicker  will  be  sufficient. 

When  the  back  tube-sheet  is  separated  from  the  fire-box 
throat-sheet  the  latter  should  be  made  the  same  thickness  as 
the  fire-box  side  sheets,  viz.,  TV'- 

The  fire-box  crown-sheet  is  usually  made  \"  and  the  side 
and  door  sheets  TV  thick. 

Diameter  d  of  Rivet-hole. — It  is  very  desirable  in  design- 
ing riveted  joints  to  obtain  the  highest  efficiency  and  still 
maintain  a  proper  tightness  by  using  a  pitch  not  too  long  for 
calking. 

In  determining  the  diameter  d  of  the  rivet  it  is  necessary 
that  it  should  be  strong  enough  to  resist  both  shearing  and 
crushing.  Now  the  resistance  to  shearing  is 

*£• 

4J 

while  that  of  crushing  is 

dtfc, 

which  shows  that  the  latter  increases  as  the  diameter  and  the 
former  as  the  square  of  the  diameter.  So  that  if  we  can  ob- 
tain such  a  relation  between  the  length  of  the  pitch  and  the 


RIVETS  AND    RIVETED  JOINTS. 


'35 


diameter  of  the  rivet-hole  as  will  give  the  highest  efficiency 
consistent  with  tightness  the  crushing  strength  of  the  rivet 
or  the  plate  in  front  of  the  rivet  need  not  be  considered. 

To  our  knowledge  the  maximum  limit  for  the  length  of 
pitch  that  will  insure  perfect  tightness  of  the  joint  has  never 
been  ascertained  by  experiment  or  test,  so  that  we  have  to 
depend  largely  on  existing  practice  in  determining  the  ratio 
between  d  and  t. 

Mr.  Wm.  M.  Barr  in  his  "  Boilers  and  Furnaces"  gives 
the  following  ratios  between  the  thickness  of  the  plate  and 
the  diameter  of  the  rivet  for  single-riveted  lap-joints,  using 
the  nearest  even  sixteenths  of  an  inch,  for  steel  plates  and 
steel  rivets  (tensile  strength  of  plates  55,000  Ibs.  and  shearing 
strength  of  rivets  44,625  Ibs.  per  square  inch): 

TABLE  14. 


Pitch  oi 

Rivets. 

•       i 

A              f  J 

rfto  *. 

d 

Equivalent. 

Sq.  In. 

Decimal. 

Working 
Fraction. 

1  H 
T 

2.75 

11" 

.6875 

•371 

I.8Q2 

If" 

A" 

2.40 

1" 

•  75 

.442 

1.897 

l|" 

£ 

2.17 

2.00 

$T 

.8125 
.875 

.518 
.601 

1-934 
1.990 

III" 
2'' 

i- 

.87 
.78 

IP" 

•9375 

1.  000 

.690 

.7854 

2.058 
2.133 

2? 

V' 

.70 

IT1ff" 

1.0625 

.887 

2.2l>5 

2TY' 

.64 

IF 

1.  125 

•994 

2.298 

2TV' 

* 

•58 

IT8/' 

1.1875 

1.108 

2.386 

2f" 

A  committee  of  the  Railway  Master  Mechanics'  Associa- 
tion on  riveted  joints  in  1895  gave  the  following  ratios  between 
d  and  /  in  their  report  for  single-riveted  lap-joints  (steel  plates 
of  55,000  Ibs.  tensile  strength  and  iron  rivets  of  38,000  Ibs. 
shearing  strength  per  square  inch) 


136 


DRAWING   AND   DESIGNING. 
TABLE   15. 


/ 

Ratios. 

Mean  Ratios. 

d 

> 

^ 

£ 

2.25  to  3.00 

2.OO  tO  2.8O 

2.62 
2.40 

f 

if" 

58.6$ 

55-8^ 

r 

2.0O  tO  2.6O 

2.30 

7" 

¥ 

2" 

55-  3# 

yV 

1.71  to  2.42 

2.O6 

w 

2Tv; 

52.8$ 

r 

1.75  to  2.35 

2.05 

l" 

»*" 

51.5* 

iV 

1.77  to  2.33 

2.05 

lyY' 

*A" 

530* 

i" 

1.  6O  tO  2.IO 

1.85 

iiV 

2lV" 

50.2$ 

Pitch  /  of  Rivets. — The  total  strength  of  a  boiler-plate 
is  reduced  by  the  rivet-holes,  and  the  shorter  the  pitch  the 
weaker  the  plate,  but  on  the  other  hand  if  the  pitch  is  too 
long  the  rivet  will  shear  unless  it  is  increased  in  diameter  to 
correspond  in  shearing  strength  to  the  tensile  strength  of  the 
net  section  of  plate,  but  a  long  pitch  and  large  rivet  diameter 
are  also  limited  by  the  fact  that  under  high  pressures  such  a 
joint  is  hard  to  make  tight. 

The  mean  ratios  between  the  thickness  /  of  plate  and  the 
diameter  d  of  the  hole  given  in  Table  15  are  recommended 
as  good  modern  practice. 

To  find  the  pitch/  in  terms  of  the  thickness  of  the  plate 
/  and  the  diameter  d\ 


(6) 


Exercise  30. — Design  a  single-riveted  lap-joint  for  a  boiler 
48"  diameter  and  carrying  a  steam-pressure  of  148  Ibs.  per 
square  inch,  plates  to  be  soft  steel  of  55,000  Ibs.  tensile 
strength  per  square  inch  and  iron  rivets  of  a  shearing  strength 
=  38,000  Ibs.  per  square  inch.  Scale  6"  —  i  foot. 

(l)  Find  thickness  t  of  plate  by  formula  5,  page  132. 


RIVETS  AND   RIVETED  JOINTS. 


137 


(2)  Determine  diameter  d  of   rivet   from   the  mean  ratio 
in  Table  15. 

(3)  Calculate  the  pitch/  by  formula  6,  page  136. 


Section  at  SJS. 


FIG.  97. 

Make  complete  drawings  as  shown   in  Fig.  97,  giving  ac- 
tual dimensions  in  place  of  letters. 

Single- riveted  lap-joints  are  commonly  used  for  circumfer- 
ential seams  of  steam-boilers. 

To  determine  whether  a  circumferential  seam   should   be 
single-  or  double-riveted  let  us  take  the  following  example: 

Diameter  of  boiler  48". 

Steam-pressure  per  square  inch  148  Ibs. 

Diameter  of  rivet  =  .875". 

Pitch  =2". 

Thickness  of  plate  =  .375". 

The  total  force  will  be 

.7854/}JP=i  1809.6  X  148  =  267,820.8  Ibs.        .     (7) 

The  resistance  due  to  the  rivets 


.     .     .     .     (8) 


DRAWING   AND    DESIGNING. 

n  =  the  number  of  rivets  in  the  circumferential  seam. 
F—  the  factor  of  safety  =  6. 
Therefore,  substituting,  we  have 


=  285,475  Ibs., 


and,  subtracting  the  force  from  the  resistance,  we  have  a  dif- 
ference of  17,654.2  Ibs.  in  favor  of  the  rivets. 
The  total  resistance  of  the  plate  is 

(p-d)  X  txft  X  n  _  1.125  X  -375  X  55>ooo  X  75 

F  6   '  (9) 

=  288,750  Ibs., 

and,  subtracting  the  total  force,  267,820  Ibs.,  from  288,750, 
there  remains  a  difference  of  20,929  Ibs.  in  favor  of  the  plate, 
which  shows  that  a  single-riveted  lap-joint  is  strong  enough 
for  the  circumferential  seams  of  a  boiler  of  the  above  dimen- 
sions. 

Prof.  Lanza  referring  to  the  efficiency  of  riveted  joints  in 
his  "  Applied  Mechanics"  says: 

"  A  riveted  joint  of  maximum  efficiency  should  fracture 
the  plate  along  the  line  of  rivets,  for  it  is  clear  that  if  failure 
occurs  in  any  other  manner,  as  by  shearing  the  rivets  or  tear- 
ing out  the  rivet-holes,  there  remains  an  excess  of  strength 
along  the  line  of  riveting,  or,  in  other  words,  along  the  net 
section  of  plate  —  if  in  a  single-riveted  joint  —  which  has  not 
been  made  use  of;  but  when  fracture  occurs  along  the  net 
section  an  excess  of  strength  in  other  directions  is  imma- 
terial. 


RIVETS  AND    RIVETED  JOINTS.  139 

"If  the  strength  per  unit  of  metal  of  the  net  section  is 
constant  it  would  be  a  very  simple  matter  to  compute  the 
efficiency  of  any  joint,  as  it  would  be  merely  the  ratio  of  the 
net  to  the  gross  areas  of  the  plate. 

"  The  tenacity  of  the  net  section,  however,  varies  and  this 
variation  extends  over  wide  limits." 

This  being  so,  the  pitch  in  the  last  example  is  slightly 
longer  than  is  necessary. 

Double-riveted  Lap-joints.  —  The  arrangement  of  the 
rivets  in  Fig.  98  is  called  chain  riveting  and  in  Fig.  99  zigzag 
riveting.  The  double-riveted  joint  is  stronger  than  the 
single-riveted  joint  because  of  the  greater  net  section  of  plate 
and  smaller  diameter  of  rivet-holes.  All  longitudinal  seams 
in  steam-boilers  should  be  at  least  double-riveted.  Steel 
plates  and  iron  rivets  are  considered  the  safer  practice  because 
of  the  danger  of  overheating  the  steel  rivets. 

Wm.  M.  Barr  in  his  "  Boilers  and  Furnaces"  referring  to 
the  heating  of  steel  rivets  says:  "  It  is  important  that  steel 
rivets  be  uniformly  heated  throughout,  and  not  the  points 
merely,  as  is  the  ordinary  method  of  heating  iron  rivets; 
neither  should  they  be  heated  as  highly  as  iron  rivets,  and 
should  never  exceed  a  bright  cherry-red.  Particular  attention 
should  be  given  to  the  thickness  of  the  fire. 

"  If  excluded  from  free  oxygen  steel  cannot  be  burned; 
if  the  temperature  is  high  enough  it  can  be  melted ;  but  burn- 
ing is  impossible  in  a  thick  fire  with  moderate  draft." 

Chain  riveting  with  rivets  of  the  same  pitch  has  been  found 
by  experiment  to  be  stronger  than  the  zigzag  riveting.  See 
Barr's  "  Boilers  and  Furnaces,"  page  85,  where  it  states  that 
the  lap  is  wider  for  chain  riveting,  "and  no  doubt  the  fric- 


I4O' 


DRAWING   AND    DESIGNING. 


tion  of  this  wider  joint  contributes  towards  the  observed  in- 
crease in  strength,"  but  the  late  D.  L.  Barnes  and  others  who 
have  tested  riveted  joints  state  that  the  friction  between  the 
plates  cannot  be  considered,  because  long  before  the  ulti- 
mate strength  of  the  lap  is  reached  the  plates  are  so  far  apart 
that  "  you  can  stick  a  knife-blade  between  them."  The  zig- 
zag riveting  is  preferred  in  locomotive-boiler  seams,  because 
the  joints  are  tighter  under  the  high  pressures  carried  than 
they  would  be  with  the  wider  lap  of  the  chain  riveting. 


25' 


Section  atSS. 

FIG.  98. 

Exercise  31 — Make  the  drawings  for  a  double-riveted  lap- 
joint,  chain  riveting,  like  Fig.  98,  except  that  the  actual  di- 
mensions should  be  given  instead  of  the  letters  shown.  Steel 
plates  and  iron  rivets.  Thickness  of  plate  =  £",  p  —  3T5^  ', 
d=  if,  /=  iK  r'  =  2</+i",  R  =  30".  Scale  6"  =  I  ft. 
Calking  need  not  be  shown  now. 

Calculate  the  efficiency  of  this  joint  in  comparison  with 
the  strength  of  the  plate. 


RIVETS  AND   RIVETED  JOINTS.  14! 

Taking  ft  at  55,000  and/*  at  38,000  as  before,  the  total 
strength  of  solid  plate  is 

/  X  /  Xft  =  3-3125  X  .625  X  55.000  =  no,ooo  Ibs. 
The  strength  of  the  net  section  of  plate  is 

(p-dyf*  =(3- 3125-  1. 125). 625  X  55,ooo  =  75,735. 
The  shearing    strength  of  the  rivets  —  .7854^JX  38,000  X 2 
(for  2   rivets)  =  75,544,  nearly  equal  to  the  strength  of  the 
net  section  of  the  plate.     Therefore  the  efficiency  of  the  joint 
is  equal  to 

E  =  75>544  =  69  per  cent  nearly. 
110,000 

The  following  ratios  of  d  to  /  for  double-riveted  joints 
were  calculated  from  the  report  of  a  committee  on  riveted 
joints  to  the  Am.  Ry.  M.  M.  Association  in  1895  : 

TABLE  16. 


• 

Ratios, 
Max.  and  Mm. 

Ratios, 
Mean. 

d 

P 

a 
Area  of  Rivet. 

* 

r  (-375) 
A"  (-4375) 

2.OO  tO  2.66 

.71  to  2.42 

2-33 
2.06 

& 

$" 

.6 
.69 

71.4 
69.7 

i"  (-5) 

•75  to  2.375 

2.063 

I  fa" 

34" 

.8866 

69.6 

A"  (-5625) 

.77  tO  2.22 

1.99 

l\" 

Si's" 

.994 

68.4 

I"  (-625) 

.60  tO  2.00 

1.  80 

if 

3lV' 

•994 

660 

tt"  (-6875) 

.54  to  1.909 

1.72 

3i  e" 

1.107 

64.7 

f"  (-75) 

.416  to  1.75 

I.58 

IT8," 

3t" 

1.107 

62.7 

To  find  titot  pitch  p  for  double-riveted  lap-joints  with  steel 
plates  and  iron  rivets. 


To  find  the  distance  between  the  centres  of  rows  of  rivets 
r  (Fig.  99). 


142  DRAWING   AND   DESIGNING. 

2 p  O-  d 
Prof.  Kennedy  gives  for  the  diagonal  pitch,    r  may 

be  found  graphically  or  calculated  by  formula 


r_ 


Table  17  gives  the  distances  (r)  calculated  by  this  formula 
for  the  different  sizes  of  rivets. 

Exercise  32 — Make  drawings  as  per  Fig.  99  of  a  double- 
riveted  lap-joint,  zigzag  riveting.  t  =  •$",  ratio  of  d  to  t  = 


Section  at  SS. 


FIG.  99. 

1. 80,  R  —  30".      /  =  \\d  in  even  TV'.      Scale  6"  —  i  foot. 

Find  r  by  formula  11.      Find/  by  formula  10. 

Exercise  33. — Make  drawings  similar  to  those  in  Fig.  100 
showing  the  junction  of  a  double  zigzag-riveted  longitudinal 
seam  with  a  single-riveted  circumferential  seam  for  a  steam- 
boiler,  t  —  TV',  d  calculated  from  the  mean  ratio  in  Table  16, 
/  to  be  determined  from  formula  10,  p'  from  Table  14,  R  = 
29",  T  may  be  calculated  from  formula  11.  Scale  6"  =  i  foot. 
Actual  dimensions  to  be  placed  on  drawing  where  letters 


RIVETS   AND    RIVETED  JOINTS. 


143 


show  in   figure.      Steel   plates   and   iron  rivets.      Finish  sheet 
according  to  directions  given  on  pages  19  and  20. 

Lap-joints  with  Inside  Welt-strip. — This  style  of  rivet- 
ing, shown   in   Fig.   IOI,  is  used  for  both  single-  and   double- 


Section  a/S£ 


'IG.     1OO. 


riveting  and  possesses  some  of  the  features  of  the  butt-  ana 
lap-joint.  In  the  single-riveted  joint  of  this  kind  the  middle 
row  of  rivets  which  rivet  the  three  thicknesses  of  plate  should 
be  spaced  according  to  the  rule  given  for  /  in  the  single- 
riveted  lap-joints  on  page  136  and  the  spacing  of  the  outer 
rows  =  2p. 

These  joints  are  better  than  the  simple  lap-joint,  but  are 
more  expensive,  and  are  not  any  better  than  the  butt-joint 
(Fig.  102),  which  is  simpler  and  less  expensive. 


144 


DRAWING   AND   DESIGNING. 


The  double-riveted  lap-joint  with  inside  welt  (Fig.  101) 
may  fail  in  any  one  of  the  following  ways : 

(1)  By  shearing  the  rivets  holding  plate  (a). 
Resistance  against  shearing  =  ^a  X  f,  =  Sa  X  38,000.       (12) 

(2)  By  tearing  plate  (a)  along  the  outside  row  of  rivets. 
Resistance  against  tearing  plate  as  above 

=  (2/  -  d]t  Xft  =  (2p  -  d]t  X  55,000.   .     .     (13) 

(3)  By  tearing  plate  (a)  along  the  intermediate  row  -f-  the 
shearing  of  one  rivet. 

Resistance  =  (2p  —  2a)t  X  55,ooo.       .     .     (14) 
Strength  of  solid  plate  =  2p  X  t  X  ft-  •      •      (16) 

_  least  resistance 

"  strength  of  solid  plate*  '      *      *     t      \™. 

Exercise  34. — Make  complete  drawings  of  a  double-riveted 
lap-joint  with  inside  welt,  zigzag  spacing,  Fig.  IOI.  The 
sectional  view  of  this  figure  is  wrongly  projected  with  inten- 
tion. Student  must  make  correct  projection. 

Take  the  remaining  dimensions  from  the  following  table : 

TABLE  17. 

DOUBLE-RIVETED    LAP-JOINTS    WITH    INSIDE    WELTS. 


t 

d 

> 

m 

r 

h 

A^ 

Efficiency. 

I" 

15" 

si" 

H" 

2yy 

3.« 

12" 

87.0 

¥ 

4" 

4" 

i'r 

2?;' 

4^'" 

i,f 

85-5 
8^.8 

V 

If 

1" 

y 

2iV' 

2|" 

4f" 

4* 

if 

85.0 
84-3 

The  Double-riveted  Butt-joint  with  Inside  and  Outside 
Welts. — This  style  of  joint  is  a  very  common  one  for  longi- 


RIVETS  AND   RIVETED  JOINTS.  145 

tudinal  seams  of  steam-boilers  with  plates  £ "  thick  and  over. 
As  shown  by  Fig.  102,  the  boiler-shell  is  rolled  to  a  perfect 
cylinder  and  the  two  edges  of  the  plate  which  butt  together 


FIG.  101. 

are  held  by  two  welt-strips  riveted  to  each  other  and  to  the 
ends  of  the  plate. 

In  a  repeating  section  of  the  plate  =  2p  there  are  two 
rivets  in  double  shear  and  two  half  rivets  in  single  shear. 

From  experiments  made  by  the  English  Admiralty  and 
others  it  has  been  demonstrated  that  I  rivet  in  double  shear 
is  equal  to  2  rivets  in  single  shear.  For  convenience  we  will 
assume  this  to  be  so  at  present,  although  it  is  quite  usual  for 
designers  of  steam-boilers  to  use  a  value  of  from  1.75  to  1.90 


146  DRAWING   AND    DESIGNING, 

for  rivets  in  double  shear;  and,  as  the  latter  values  agree  more 
nearly  with  general  practice  for  butt-joints,  it  will  be  neces- 
sary for  us  to  modify  our  proportions  in  this  regard,  as  will 
appear  later.  Therefore  to  prevent  the  plate  a  pulling  out 
from  between  the  welt-strips  the  resistance  to  shearing  will  be 

5  X  a  X  fs  , 

there  being  two  rivets  in  double  shear  and  two  half  rivets  in 
single  shear  =  5  areas  in  single  shear. 

Resistance  to  tearing  the  net  section  of  plate  at  the  outer 
row  is 

(2P-d}tft. 

Resistance  to  tearing  the  plate  between  the  inner  row  of 
rivets  and  shearing  rivets  in  outer  row  is 

(2p-2d)t  Xft  +  iaft. 
Resistance  to  crushing  the  plate  in  front  of  3  rivets  is 

ltd/..- 

fc  may  be  taken  at  80,000  Ibs.  per  square  inch  for  iron 
and  90,000  for  steel  rivets. 

Strength  of  whole  plate  equal  in  width  to  2p  is 

2p  X  *  X  ft  . 

Exercise  35.  —  Draw  elevation  and  cross-section  of  a  double- 
riveted  butt-joint  with  outer  and  inner  welts  similar  to  Fig. 
1  02,  given  /  =  T9T",  d  =  1.92  A 

If  we  consider  the  resistance  to  tearing  equal  to  the  resist- 
ance to  shearing,  then 


but  this  makes  the  pitch  too  long,  because  of  the  excess  of 
strength  in  the  rivets  against  shearing.     A  better  proportion 


RIVETS  AND   RIVETED  JOINTS.  •  1 47 

and  one  that  conforms  to  good  practice  is 

\--:  .:;•"••  v=*^+*-W    : 

/j  and  /,  are  usually  equal  to  /,  but  occasionally  /,  will  be 


FIG.  102. 

found  TV'  thicker  than  /.  The  Hartford  Steam-boiler  In- 
spection &  Insurance  Company  give  all  welt-strips  -£$"  less 
in  thickness  than  t. 

For  the  remaining  dimensions  see  the  following  table : 

TABLE  18. 

For  double-riveted  butt-joints  with  outer  and  inner  welt-strips. 


Ratio  of 
d  to/. 

Diameter 
of  Hole. 

Pitch. 

g 

-2/ 

^ 

^ 

Average. 

d 

' 

3" 

2.19 

H" 

2iV' 

'*; 

2f" 

4f; 

9i" 

7  " 

1-93 
1.92 
1.92 
1.72 

| 

$ 

i 

1' 

12" 

148 


DRA  WING   AND    DESIGNING* 


Triple-riveted  Butt-joint  with  Outer  and  inner  Welt- 
strips  (Fig.  103). — This  joint  has  three  rows  of  rivets  on  each 
side  of  the  butt.  One  row  passes  through  the  boiler-plate 
and  one  welt-strip  and  two  rows  pass  through  the  sheet  and 
two  welts. 

The  resistance  to  tearing  along  line  xx  is 


t 


FIG.  103. 

The  resistance  to  pulling  the  plate  out  from  between  the 
welt-strips  is 

9X  a  X/f  X  .85. 


RIVETS  AND    A1VETED  JOINTS.  149 

The  resistance  to  tearing  on  line  yy  -and  shearing  rivets 
on  xx  is 

(2p-2d)tft  +  laf,. 

A  glance  at  the  figure  will  show  that  this  joint  cannot  fail 
along  the  line  zzy  because  there  are  two  rivets  in  double  shear 
and  one  rivet  in  single  shear  in  addition  to  the  net  section  of 
plate,  which  is  equal  to  the  net  section  on  yy. 

Exercise  36. — Make  the  drawings  for  a  triple-riveted  butt- 
joint  like  Fig.  103.  Steel  plates  and  iron  rivets.  /  =  £", 
d =  ij".  Scale  4!'  =  I  foot.  The  other  dimensions  may  be 
taken  from  the  following  table : 

TABLE  19. 


>  In. 
* 


T> 

i 


In. 

'•? 

ft 

I 

k 
I 


I 


If 


In. 


3* 
33 
31 
31 

34 

31 


4V 

4T¥ 


In. 

il 


If 


In. 

I 


2T1* 


2| 


IT'* 


IT** 
If 


2| 

2| 


In. 

81 
9* 


9* 

ioi 


ioi 

III 

12 

10} 

III 

12 

12* 

12 


I3f 

14 

14 


N 

In. 

M 


17 

I7i 


20± 


Efficiency. 


Per  Cent. 
86.1 
86.2 
86.1 
86.2 
86.2 
,86.1 
86.2 
86.2 
86.2 
86.2 
-  86.1 
86.2 
86.2 
86.1 
86.2 
86.3 
86  2 
86.3 
86.1 
86.1 
86.2 
86.2 


Calculate  efficiency  and  if  possible  show  where  improve- 
ment might  be  made. 


ISO 


DRA  WING   AND   DESIGNING. 


Exercise  37 — Draw  the  junction  of  a  longitudinal  double- 
riveted  butt-joint  with  a  single-riveted  circumferential  lap- 
joint  (Fig.  104).  t  =  f",  d  —  -if".  The  remaining  dimen- 
sions may  be  taken  from  Tables  18  and  14..  Scale  6"  —  i  foot. 


FIG.  104. 

Exercise  38 — Make  drawings  of  the  staying  for  the  back- 
head  and  fire-box  crown-sheet  of  a  locomotive-boiler  as  shown 
by  Fig.  105.  Scale  jff  —  /  foot. 

This  is  an  example  of  what  is  known  as  the  croivn-bar 
staying  for  locomotive-boilers.  The  design  is  suitable  for  an 
engine  with  cylinders  19"  X  24",  steam-pressure  180  Ibs.  per 
square  inch,  and  is  similar  to  that  used  in  the  Empire  State  Ex- 
press locomotive  designed  by  Wm.  Buchannan,  Supt.  of  Motive 
Power  of  the  N.  Y.  C.  R.  R.  A  A  shows  a  cross-section 
and  a  partial  elevation  of  one  crown-bar  which  consists  of  two 


RIVETS  AND   RIVETED  JOINTS.  !$! 

wrought-iron  plates  5"  deep  X  f  "  thick  and  welded  together 
at  the  ends.  The  fire-box  crown-sheet  is  supported  by  f  " 
rivets,  which,  passing  through  a  washer  b  and  between  the 


j  IRON  LINER. 


plates  A  of  the  bar  and  through  thimble  G,  is  riveted  on  the 
under  side  of  the  crown-sheet  as  shown.  These  rivets  are  placed 
from  4"  to  4i"  apart,  and  as  many  as  the  crown-bars  will  ac- 
commodate at  these  centres,  the  end  bolts  being  placed  about 
4"  from  the  inside  of  the  fire-box  side  sheets.  As  seen  from 
the  figure,  the  crown-bars  are  placed  in  a  transverse  position 


152  DRAWING   AND   DESIGNING. 

on  the  crown-sheet,  and  as  many  as  the  longitudinal  length  of 
the  sheet  will  allow,  with  equal  spacing,  about  4^"  apart. 
Should  these  bars  be  insufficient  to  support  the  crown-sheet 
against  the  downv/ard  pressure  of  the  steam,  which  is  equal 
to  the  area  of  the  crown-sheet  X  the  steam-pressure  per  square 
inch,  then  what  remains  is  held  up  by  sting-stays  hung 
from  the  outer  shell  and  fastened  to  the  crown-bars  by  links 
and  pins,  one  link  of  which  is  shown  at  d  in  the  transverse 
cross-section. 

The  flat  upper  part  of  the  back-head,  which  has  no  stay- 
bolts  passing  through  it  like  those  which  bind  the  fire-box  and 
outer  shell  together,  as  shown  at  D,  is  stiffened  with  a  liner 
•f"  thick,  the  shape  of  which  is  shown  by  dotted  lines  on  the 
transverse  section,  and  to  this  liner  are  riveted  as  many  lengths 
of  3/r  X  3"  angle-iron  as  can  be  placed  on  the  liner,  with  a 
clearance-space  of  only  about  f"  between.  To  these  angle- 
irons  are  bolted  longitudinal  stay-rods  i-J"  in  diameter  similar 
to  that  shown  in  Fig.  106. 

To  support  that  curved  part  of  the  outside  shell  just  above 
the  fire-box  transverse  stay-rods  C  are  carried  between 
each  crown-bar,  screwed  through  the  shell  on  each  side,  and 
riveted  over  on  the  outside.  The  body  of  the  rod  is  \\"  in 
diameter  and  the  screwed  ends  I J"  diameter. 

The  fire-box  stay-bolts  D  are  screwed  through  both  fire- 
box and  outer  shell  and  riveted  over  outside  and  inside.  It 
will  be  seen  that  while  the  screwed  part  of  the  bolt  is-J"  diam- 
eter the  body  is  turned  down  to  f ",  which  reduces  its  stiffness 
and  allows  it  to  give  somewhat  to  the  unequal  expansion  of 
the  fire-box  and  outer  shell  of  the  boiler.  In  certain  places 
the  stay-bolts  are  more  liable  to  break  than  in  others ;  in  such 


RIVETS  AND    RIVETED  JOINTS.  153 

places   hollow  stay-bolts  are   used,  so  that  when  broken  they 
may  be  easily  and  quickly  detected. 


Hollow    stay-bolts    have    an  -J"  hole    drilled    completely 
through  from  fire-box  to  the  outside  of  the  outer  shell,  so  that 


154 


DRAWING   AND   DESIGNING. 


if  one  should  break  the  escaping  steam  and  water  will  soon 
inform  the  engineer. 

A  detail  view  of  one  of  the  crown-bar  thimbles  is  shown 
at  G. 

Construction. — Draw  the  perpendicular  centre  line  6'  6" 
from  the  left-hand  margin,  and  the  longitudinal  centre  line 
4'  6"  from  the  upper  margin  ;  then  draw  the  transverse  and 

4* 


FIG.  107. 

longitudinal  cross-sections  of  the  boiler  and  construct  the 
crown-bars  and  other  staying  as  shown. 

It  will  be  seen  in  the  figure  that  where  the  plates  should 
come  together  they  have  been  left  slightly  apart ;  this  is  a 
convention  followed  by  draftsmen  to  facilitate  inking  without 
blots  and  to  improve  the  appearance  of  the  drawing. 

Exercise  39. — Fig.  106  gives  an  example  of  a  longitudinal 
stay-rod  with  details  and  a  crow-foot  for  a  locomotive-boiler. 
Make  the  drawings  to  a  scale  of  6"  =  /  foot. 


RIVETS  AND   RIVETED  JOINTS. 


155 


Exercise  40. — Figs.  107  and  108  show  examples  of  riveting 
the  corner  of  a  locomotive  fire-box  ring  (sometimes  called  a 


FIG.  108. 


s~  COP  PEP. 


M- 


TT 


FIG.  109. 

mud-ring)   to   the  bottom  of  the  fire-box  and  outer  shell  of 
the   boiler.     Fig.  108   is  that  of  a  large  boiler  58"  diameter 


156 


DRAWING   AND    DESIGNING. 


and  carrying  180  Ibs.  steam-pressure  per  square  inch,  and 
Fig.  107  is  for  a  smaller  boiler  of  48"  diameter  at  waist. 
Make  drawings  of  both  figures  as  shown  to  a  scale  0/4."  =  i 
foot. 

Exercise  41. — Fig.  109  shows  the  setting  of  a  tube  in  the 
front  and  back  tube-sheets  of  a  fire-tube  boiler  for  a  locomo- 
tive. Both  ends  show  the  tubes  swedged,  rolled,  and  beaded, 
and  with  copper  ferrules  between  the  tubes  .and  the  sheets. 
Make  a  drawing  like  that  shown  by  the  figure  to  the  scale  of 
full  size. 

Fig.  no  is  a  section  of  a  locomotive-boiler  dome,  dome- 
ring  C  and  dome-base  B.  The  base  and  ring  are  made  of  soft 
steel  and  formed  in  dies  by  hydraulic  pressure. 


4  RIVET 


Exercise  42 — Make  half  sectional  elevation,  half  outside 
elevation  with  transverse  view  and  plan.  Also  show  the 
curves  of  intersection  between  the  dome-base  and  boiler. 
Scale  2"  =  i  foot. 


CHAPTER    IV. 
SHAFTING   AND   SHAFT-COUPLINGS. 

UNDER  the  term  shafting  may  be  included  line  shafting 
and  axles. 

Line  Shafting. — This  name  is  given  to  the  long  line  of 
rotating,  cylindrical  or  square  shafting  used  in  workshops  and 
factories  for  transmitting  turning  power  or  twisting  moments 
from  the  prime  movers.  They  are  in  some  ways  an  extension 
of  the  prime  mover.  Such  shafting  is  subjected  to  torsional 
and  bending  stresses,  the  latter  being  due  to  the  pull  of  belts 
and  the  weight  of  pulleys,  gears,  levers,  etc.  "It  is  usual  to 
make  line  shafting  of  uniform  diameter  throughout,  as  shown 
in  Fig.  ill,  enlarged  ends  being  only  used  occasionally  for 


FIG.  in. 

exceptional  purposes.  Steel  of  a  grade  containing  .3  to  .4^ 
of  carbon  is  now  used  almost  entirely  for  shafting  in  prefer- 
ence to  iron  in  this  country.  The  commercial  lengths  of 
shafting  for  ordinary  diameters,  as  from  2"  to  3".  run  from 
1 6  ft.  to  30  ft.,  the  shorter  lengths  being  more  convenient  for 
transportation,  for  replacing  pulleys,  gears,  etc.  But  the 


158 


DRAWING  AND   DESIGNING. 


longer   lengths  are   frequently  used  when   objections  do  not 
arise  from  these  considerations."  * 

Torsional  or  Twisting  Moment. — Figs.  112  and  113 
show  a  lever,  a  gear  wheel  and  pinion  keyed  to  their  respec- 
tive shafts;  R  is  the  radius  of  the  lever  and  the  pitch  circle 
of  the  gear  through  which  the  power  P  is  transmitted.  This 
force  P  produces  a  twisting  action  on  the  shaft,  and  the  prod- 
uct RP  is  called  the  torsional  moment  (T)  on  the  shaft. 


FIG.  112. 


FIG.  113. 


FIG.  114. 


So  in  Fig.  1 14  P  is  equal  to  the  tension  T,  —  Tt,  and  the 
radius  R  multiplied  by  the  force  P  is  again  equal  to  the 
torsional  moment  on  the  shaft.  The  torsional  moment  is 
usually  expressed  in  inch-pounds,  i.e.,  the  force  Pin  pounds 
into  the  radius  R  in  inches  is  equal  to  the  torsional  moment 
in  inch-pounds. 

The  moment  of  resistance  to  torsion  of  a  cylindrical  shaft 
is  equal  to  the  greatest  stress  multiplied  by  the  modulus  of 
the  section. 

Let  Ft  be  the  greatest  shearing  stress  and  Zt  the  modulus ; 
then 

T=FsZt (I) 


*  A.  &  P.  Roberts  Company. 


SHAFTING   AND    SHAFT-COUPLINGS. 


I  $9 


and 


Z<  =  77^'=  •  19635^; 


so  for  cylindrical  shafts 

T=  .19635^,       ......     (2) 

and  for  square  shafts 

T=.2oMy.;    ..     .     .     .     .     .     .     (3) 

d  =  diameter  of  the  cylindrical  shaft  and  length  of  side  of 

square  shaft  in  inches; 

f,  =  shearing  strength  in  pounds  per  square  inch; 
T  =  torsional  moment  in  inch-pounds. 

To  Find  the  Diameter  of  a  Wr  ought-iron  or  Steel 
Shaft.  —  If  we  take  the  resistance  to  shearing  for  iron  equal 
to  40,000  Ibs.  per  square  inch  and  for  soft  steel  at  50,000 
Ibs.,  and  using  a  factor  of  safety  of  4^,  we  have: 

For  cylindrical  iron  shafts    T  =  i/2O^3; 

For  cylindrical  steel  shafts  T=  2182^'; 

For  square  iron  shafts  T=  i849^/3; 

For  square  steel  shafts          T=  231  \d*. 


Then 


d= 


I  720 


for  cylindrical  iron  shafts ; 


V 


^^ 

for  square  iron  shafts;    . 


V 


1849 

~T~ 
2182 

f~ 
23"" 


for  cylindrical  steel  shafts; 
for  square  steel  shafts.    . 


(4) 
(5) 
(6) 
(7) 


160  DRAWING   AND    DESIGNING. 

Example  i. — Let  the  pitch  diameter  of  a  spur  gear  on  an 
iron  shaft  be  60",  and  the  total  pressure  on  the  teeth  at  the 
pitch  line  2500  Ibs.  What  would  be  the  diameter  of  the 
shaft  and  the  horse-power  transmitted  by  the  wheel  if  running 
at  the  fate  of  140  revolutions  per  minute  ? 

From  equation  (4)  we  get 


d  = 


for  the"  horse-power  transmitted  by  the  wheel. 

Let    H.P.  =  horse-power  —  33,000  X    12  =  396,000    inch- 

pounds; 

n  =  number  of  revolutions  per  minute; 
then 

PX  n 


'-  -    396,000     '   ' 

_  6.28  X  Tx  n  _  6.28  X  75,000  X  140 
396,000          396,000 

In  terms  of  the  H.P., 


'  •   ' 
_ 


and 


H.P. 


Besides  the  twisting  stresses  on  shafts  which  we  have  alone 
taken  account  of  in  the  above  formulae,  there  is  usually  a 
bending  moment  to  be  considered.  Let  a  shaft  be  subjected 


SHAFTING  AND  SHAFT-COUPLINGS.  l6l 

to  a  torsional  moment  T  and  supporting  a  bending  moment 
B  ;   these  two  stresses  will  be  equal  to  a  twisting  moment 


Tl  is  called  the  equivalent  twisting  moment,  and  should 
be  used  in  place  of  T  in  figuring  the  diameter  of  a  shaft  sub- 
jected to  combined  torsion  and  bending.  The  "bending 
stresses  in  revolving  shafts  are  continually  changing  from 
tension  to  compression  and  from  compression  to  tension,  so 
that  for  combined  bending  and  twisting  the  factor  of  safety 
4^  given  for  twisting  alone  should  be  increased  in  the  follow- 
ing ratio:  When  B  is  more  than  ^Tand  not  more  than  .6T, 
the  factor  of  safety  should  be  5  ;  when  over  .6Tand  not  more 
than  T,  5J;  and  when  greater  than  7",  6. 

Example  2.  —  Determine  the  diameter  of  a  wrought-iron 
shaft  which  has  to  resist  a  torsional  moment  of  400,000  inch- 
pounds  and  a  bending  moment  of  200,000  inch-pounds.  By 
formula  (M)  the  equivalent  twisting  moment 


Tl  =  B  +  4/#*+r*  =200,000+ 

=  200,000+447,213.5=647,213.5  in.-lbs. ; 
and  by  equation  (4) 


3  /    T,          3/647,213.5 
=  =         ~  ~~ 


Example  j.-  —  When  the  bending1  moment  exceeds  the  tor- 
sional moment  .  —  A  non-continuous  steel  shaft  has  its  bearings 
8  ft.  apart  and  carries  a  pulley  of  50"  diameter  at  its  centre  ; 
the  pulley  is  driven  by  a  10"  belt,  the  effective  weight  and 


162  DRAWING  AND   DESIGNING. 

belt-pull  being  500  and  800  Ibs.  respectively.     What  should 
be  the  diameter  of  the  shaft  ? 

In  this  case  the  factor  of  safety  will  be  6  and  equation  (4) 
becomes 


B  = 


T  =  800  X  25  =  20,000  inch-lbs.  ; 


T;  =  31,200+  V  3I,200a  +  20,000'  =  68,230; 

and 


Deflection  of  Shafting. — A  maximum  deflection  of 
of  an  inch  per  foot  of  length  /for  continuous  shafting  is  given 
as  good  practice  by  the  Pencoyd  Iron  Works.  The  weight 
of  bare  shafting  =  2.6d*  X  /  =  W,  and  for  loaded  shafts, 
allowing  40  Ibs.  per  inch  of  width  for  the  vertical  pull  of  the 
belts,  W=  \$d*l.  Then  for  bending  stress  alone,  taking  the 
modulus  of  transverse  elasticity  at  26,000,000,  we  can  derive 
from  authoritative  formulae  the  maximum  length  between 
bearings 


/=   V8;3^a  for  bare  shafts;   ....     (13) 
for  loaded  shafts.     .      .      .      (14) 


SHAFTING   AND    SHAFT-COUPLINGS.  1 6- 

For  line-shafting  hangers  8  ft.  apart  Thurston  gives 


d*n  3/90  H. P.  , 

H.P.  = d  =  \  /  -  ~  for  wrought  iron; 

90  y          « 

H.P.  = d=  \  /— — ' — -  for  cold-rolled  iron. 

55         V        » 

Hollow  Shafts. — Weight  for  weight  the  hollow  shafts  are 
stronger  than  solid  shafts,  because  the  portion  of  material 
removed  is  the  least  effective  in  resisting  torsion.  The 
resistance  to  torsion  in  a  solid  shaft  and  a  hollow  shaft  will 
be  equal  when  the  moduli  of  the  sections  are  equal.  Let  d 
be  the  diameter  of  a  solid  shaft,  and  d^  and  dt  the  internal  and 
external  diameters  respectively  of  a  hollow  shaft.  Then 


A  10"  hollow  shaft  with  hollow  4"  diameter  will  weigh 
less  than  the  solid  10"  shaft,  but  its  strength  will  be  only 
2.56$  less.  If  the  hole  were  increased  to  5"  diameter  the 
weight* would  be  25$  less  than  that  of  the  solid  shaft,  and  the 
strength  only  4.25$  less. 

The  relation  between  the  weights  of  solid  and  hollow 
shafts  is  as  follows : 

Let  W '=  weight  of  hollow  shaft,  and  Wl  =  weight  of 
solid  shaft ;  then 

w    d:  -  d: 


d* 


(16) 


the  weight  of  the  hollow  shaft  in  per  cent  of  the  weight  of 
the  solid  shaft. 


164  DRAWING   AND    DESIGNING. 

And  the  difference  in  strength  is  given  as  follows  : 
Let  5  =  strength  of  hollow  shaft,  and  5A  =  strength  of 
solid  shaft  ;   then 


s; 


When  d*  =  d?  —  d?  the  solid  and  hollow  shafts  are  of  equal 
weight  ;  and  when  d*  =         .  —  -  the  solid  and  hollow  shafts 

are  of  equal  strength. 

A  hollow  shaft  is  stiffer  than  a  solid  shaft  of  the  same 
resistance  to  torsion,  i.e.,  it  does  not  yield  to  bending  as 
readily  ;  this  is  an  objection  under  some  conditions,  as  in  the 
case  of  a  steamship's  propeller-shaft,  where  it  would  be  an 
advantage  if  the  shaft  would  give  a  little  to  the  straining 
action  of  the  ship  in  a  storm. 

The  larger  hollow  shafts  are  usually  forged  hollow,  but  the 
smaller  shafts  are  forged  or  rolled  solid  and  then  bored 
hollow. 

SHAFT-COUPLINGS. 

We  have  seen  that  shafting  is  made  only  in  short  lengths 
of  about  16  ft.  to  30  ft.  long,  so  it  is  necessary  in  long  lines 
of  shafting  to  couple  these  lengths  together  by  means  of 
what  is  known  as  shaft-couplings.  There  are  three  principal 
divisions  of  shaft-couplings,  viz.,  rigid,  flexible,  and  clutch 
couplings.  All  couplings  should  be  placed  close  to  bearings 
on  the  side  farthest  from  the  driving-point. 

Rigid  Couplings.  —  When  two  shafts  are  joined  by  a 
coupling  that  can  only  be  removed  by  loosening  keys  ox 


SHAFTING   AND    SHAFT-COUPLINGS.  1 6$ 

unscrewing  bolts,  such  a  coupling  is  said  to  be  a  rigid  or  fast 
coupling. 

Box  or  Muff  Couplings. — This  is  the  simplest  kind  of  a 
shaft-coupling  (Fig.  115).  It  is  made  of  cast  iron.  The  hole 
for  the  shaft  is  cored  small  in  the  casting  and  afterwards  bored 
out  to  fit  the  finished  diameter  of  the  shaft.  The  coupling 
is  secured  to  the  shaft  by  means  of  a  wrought-iron  or  steel 
sunk  key  about  equal  in  length  to  the  coupling  itself,  or  by 
two  keys  each  about  half  as  long  as  the  coupling.  The 
latter  method  is  the  best,  because  then  it  is  not  so  necessary 
that  the  keyway  in  both  shafts  should  be  exactly  the  same 
depth ;  moreover,  the  two  keys  can  be  driven  tighter  and 
slacked  easier  than  one  long  key.  Half  the  depth  of  the 
keyway  is  cut  in  the  shaft  and  half  in  the  coupling.  The 
two  shafts  butt  together  at  the  ends.  When  two  keys  are 
used  a  clearance  space  should  be  left  between  them  when 
driven  home,  to  insure  an  equal  tightness  of  both  keys,  as 
shown  at  5,  Fig.  115. 

Exercise  43. — Make  a  complete  working  drawing  of  a  muff 
coupling  like  Fig.  115  for  a  2\"  shaft.  Scale  =  full  size. 

The  dimensions  may  be  found  from  the  following  propor- 
tions: 

d=  diameter  of  shaft  =  "2^"; 
t  =  thickness  of  metal  in  coupling  =  .4^+  i"; 
/  =  length  of  muff  =  2\d  +  2"; 
D—  d+2t. 

For  proportions  and  taper  of  key  see  page  in.  In  some 
positions  of  the  coupling  on  the  shaft  the  key  should  have  a 
gib  head,  as  shown  at  h  in  Fig.  117,  when  it  is  difficult  to 


r66 


DRAWING  AND   DESIGNING. 


SHAFTING   AND    SHAFT-COUPLINGS.  1 67 

obtain  access  to  the  small  end  for  the  purpose  of  slacking  up. 
When  the  coupling  is  situated  close  to  the  bearing  it  will 
be  necessary  to  make  the  length  of  the  keyway  to  the  left 
of  the  coupling  equal  to  half  that  of  the  corresponding 
key. 

Split-muff  Couplings.  —  Fig.  116  shows  a  form  of  coup- 
ling divided  into  two  parts  and  bolted  together  on  the  shaft, 
sometimes  called  a  compression  coupling.  It  is  keyed  to  the 
shaft  with  a  straight  parallel  key  which  fits  only  at  its  sides. 
The  length  of  the  key  may  be  £"  longer  than  the  coupling 
and  the  keyway  the  same  length  as  the  key. 

Exercise  44. — Make  working  drawings  of  the  split-muff 
coupling  shown  in  Fig.  1 16  for  a  3"  shaft.  Scale  6"  =  i  fooL 

In  finishing  this  coupling  the  inside  faces  of  the  two  halves 
are  planed  and  the  bolt-holes  drilled.  Now  placing  a  piece 
of  sheet  tin  between  the  halves  and  bolting  them  together, 
the  hole  is  bored  for  the  shaft,  making  it  equal  in  diameter 
to  the  finished  shaft.  The  sheet  tin  is  then  removed,  and  the 
coupling  when  bolted  on  the  ends  of  two  shafts  clamps  them 
very  tightly  together.  The  ease  with  which  the  split  coup- 
ling can  be  removed  and  replaced  gives  it  a  great  advantage 
over  the  solid-muff  coupling. 

Flange  or  Plate  Coupling. — Fig.  117  shows  a  plate 
coupling  made  by  the  Dodge  Mfg.  Co.  It  is  made  in  two- 
parts,  of  cast  iron,  and  keyed  to  the  two  shaft  ends,  the  posi- 
tion of  the  key  in  the  one  shaft  being  at  right  angles  to  the 
key  in  the  other.  The  bolts  are  turned  and  carefully  fitted, 
and  the  holes  drilled  to  template  so  that  they  can  be  duplicated 
if  desired.  Each  coupling  should  be  faced  after  it  has  been 
keyed  to  its  shaft,  so  as  to  obtain  perfect  alignment. 


168 


DRAWING  AND   DESIGNING. 


SHAFTING   AND    SHAFT-COUPLINGS. 


169 


I/O  DRAWING   AND   DESIGNING. 

Exercise  45. — Make  drawings  of  Fig.  117  as  shown,  ex- 
cept that  the  upper  half  of  the  end  elevation  shall  be  a  sec- 
tional view  through  XX. 

Let  D  =  diameter  of  shaft  =  2"  \ 
Unit  =  £>  +  £"; 

n  =  number  of  bolts  =  3  -\ (18) 

Taking  the  nearest  even  number, 

d  =  diameter  of  bolt  = ( .    .     .     .     (19) 


FIG.  118. 

The  remaining  dimensions  can  be  found  from  the  propor- 
tions given  in  the  figure  in  terms  of  d,  the  diameter  of  the 
bolt. 

The  taper  of  the  hub  may  be  made  equal  to  $•"  in  12". 

The  shaft  in  this  figure  is  shown  sectioned  for  wrought 
iron,  but  in  the  drawing  required  it  may  be  sectioned  with 
steel  color. 

Figs.  118  and  119  show  plate  couplings  made  by  the  Hill 
Clutch  Company. 


SHAFTING   AND   SHAFT-COUPLINGS. 


171 


Exercise  46. — Make  drawings  as  required  for  Exercise  45 
of  a  "  Hill  "  plate  coupling  for  a  4J"  shaft.  The  dimensions 
for  /2  and  ^  to  be  taken  from  Table  20.  The  number  of 


TABLE  20. 

DIMENSIONS    FOR    THE    "HILL"    PLATE   COUPLINGS. 


Diameter 
Shaft. 

A 

e 

Diameter 
Shaft. 

A 

B 

Diameter 
Shaft. 

A 

B 

I» 

7 

6 

*H 

II* 

9* 

5j 

i7i 

16 

1 

7 
8 

6 
6 

3* 

3iV 

II* 

10 

10* 

6 
6* 

20 

21 

17 

18* 

8* 

6* 

3H 

12* 

IOj 

7 

22 

20 

1 

8* 

10 

ii 

8 
84 

3tt 

5 

13 

14* 
16* 

nj 

14! 

8 
9 

10 

24 
26 
28 

22 

24 

26 

bolts  to  be  determined  from  equation  (18),  and  the  diameter 
of  the  bolts  from  equation  (19)  The  remaining  proportions 
to  be  worked  out  according  to  the  student's  judgment. 

The    Sellers    Clamp    Coupling  (Fig.    120).— This  is  a 
special  form   of  a  muff  coupling  which  is  turned  to  a  cylin- 


1/2  DRAWING   AND    DESIGNING. 

d'rical   form   on  the  outside,  but  has  a  double  conical  section 
inside.      Two    conical    sleeves    or    bushes    turned    to   fit   the 


FIG.  120. 

inside  of  the  muff  and  bored  out  to  fit  the  shafts  are  pulled 
together  by  three  bolts.  The  sleeves  are  split  on  one  side 
through  one  of  the  bolt-holes,  so  that  the  more  the  bolts  are 
screwed  up,  the  tighter  the  sleeves  clamp  the  shafts  and  bind 
them  firmly  together.  Keys  are  also  used  to  further  prevent 
slipping. 

Exercise  47. — Make  the  drawings  shown  in  Fig.  12  I  of  a 
Sellers  clamp  coupling.  Scale  full  size -. 

The  taper  of  the  conical  sleeve  is  2f"  per  foot  of  length 
on  the  diameter ;  e.g.,  if  the  sleeve  was  6"  long  and  the  large 
diameter  measured  4",  the  small  diameter  would  measure  2f ". 

For  the  dimensions  of  the  Sellers  clamp  coupling  for 
various  diameters  of  shaft,  use  the  following  table. 


SHAFTING   AND    SHAFT-COUPLINGS. 


173 


174 


DRAWING   AND    DESIGNING. 


TABLE   21. 

SELLERS    CLAMP    COUPLINGS. 


D 

y4 

B 

c 

E 

- 

D 

A 

B 

c 

.£• 

- 

I*" 

4i" 

5f" 

•r 

3l 

1«" 

3" 

8V 

III" 

41" 

61" 

1" 

If 
2 

Si 

6* 

6| 

71 

at 

3 

4| 

'      | 

3i 

4 

9J 
ii 

3) 

5i 
6 

8| 

i 

2* 

6* 

S£ 

3» 

5 

I 

5 

I2g 

18^ 

7* 

ii 

ai 

7i 

9^ 

3l 

51 

6 

Mi 

2Ii 

9 

ni 

ii 

2£ 

7* 

.oi 

4i 

6 

¥ 

Frictional  Coupling. — Fig.  122  shows  three  views  of 
Butler's  frictional  coupling.  It  is  somewhat  like  the  Sellers 
coupling,  except  that  it  has  neither  bolts  nor  keys,  the  conical 
bushes  being  held  in  position  by  round  nuts  threaded  into  the 
muff.  The  conical  bushes  are  split  at  the  side,  and  when  they 
are  in  position  on  the  shaft  the  split  sides  are  at  right  angles 
to  each  other;  this  arrangement  allows  a  key-driver  to  be 
introduced  through  one  of  these  openings  (after  the  nuts  have 
been  removed)  to  drive  out  the  other  bush  when  it  is  desired 
to  remove  the  coupling  from  the  shaft.  The  bushes  are 
guided  into  position  by  small  dowel-pins  which  enter  short 
grooves  provided  for  them  inside  the  muff.  The  \"  round 
holes  shown  in  top  and  bottom  at  the  centre  of  the  muff  are 
used  to  see  when  the  ends  of  the  shafts  come  together,  for 
then  only  will  the  coupling  be  in  its  proper  position. 

Exercise  48. — Make  complete  working  drawings  of  the 
Butler  coupling  like  Fig.  122,  except  that  the  shaft  shall  be 
of  steel  and  the  sectioning  shall  be  appropriately  colored 
instead  of  hatch-lined.  Scale  —  full  size. 

The  threads  on  the  lock-nuts  should  be  that  number  per 
inch  used  on  a  pipe  whose  outside  diameter  is  nearest  to  the 


SHAFTING  AND   SHAFT-COUPLINGS. 


DRAWING   AND   DESIGNING. 

outside  diameter  of  the  nut.  The  lock-nuts  are  screwed  into 
position  by  means  of  a  spanner  wrench  having  projecting 
pieces  which  fit  into  the  recesses  shown  in  .  end  elevation. 
The  taper  of  the  conical  bushes  may  be  made  f"  in  12"  on 
the  diameter.  The  faces  marked  with  small  f  are  to  be 
finished. 

The  principal  proportions  of  this  coupling  are  as  follows: 

d  •=  diameter  of  shaft; 
D  —  diameter  of  muff  =  2.2$d\ 
L  =  length  of  muff  =  4</. 

Stuart's  Clamp  Coupling. — This  coupling,  shown  in  Fig. 
123,   differs    from    the    Sellers    coupling    in    having   tapered 


FIG.  123. 

wedges  instead  of  conical  sleeves;  these  tapered  wedges  and 
opposite  halves  of  each  end  of  the  muff  are  bored  to  the  size 
of  the  shaft.  Studs  and  nuts  hold  the  wedges  in  place, 
making,  on  the  whole,  a  cheap  and  effective  coupling  without 
the  use  of  keys. 

Exercise  49. — Make    drawings    of  a  Stuart's  coupling  as 
shown  in  Fig.  124  for  a  if"  shaft.     Scale  =  full  size. 


SHAFTING  AND^  SHAFT-COUPLINGS. 


'77 


178  DRAWING   AND   DESIGNING. 

The    principal    dimensions    of    this   coupling   for   various 
diameters  of  shaft  are  given  in  the  following  proportions: 
"  Let  d  —  diameter  of  shaft; 
D  —  diameter  of  muff; 
L  —  length  of  muff. 
Then  for  shafts  from  i  J"  to  2f"  diameter 

D  =  3.25^,          £  =  4.25^; 
for  shafts  from  2f "  up 

£>  =  &  L  =  ±d. 

Flanged  Shaft-coupling. — Fig.  125  shows  a  propeller- 
shaft  coupling  in  which  the  flanges  are  formed  by  forging 
them  on  the  shaft. 

Exercise  50. — Make  working  drawings  of  the  flange  coup- 
ling shown  in  Fig.  125.  Assume  the  external  diameter  of  the 
shaft  to  be  18"  and  the  internal  diameter  10",  and  take  an 
equivalent  solid  shaft  as  the  unit  for  the  proportions.  Scale 
2"  =  i  foot. 

Let  Dv  and  D^  be  the  internal  and  the  external  diameter, 
respectively,  of  the  hollow  shaft;  then  from  equation  (15)  we 
have 


=  diameter  of  an  equivalent  solid  shaft  =  unit. 
<^—  diameter  of  bolt; 
n  =  number  of  bolts  =  .2$D  -|-  2 ; 

R  =  radius  of  bolt  circle  =  -  . 

Resistance  to  shearing  of  bolts  —  resistance  to  torsion  of 
shaft  divided  by  R. 


SHAFTING   AND   SHAFT-COUPLINGS. 


179 


ISO  DRAWING  AND   DESIGNING. 

From  equation  (2), 


(20) 


and  taking/,  at  50,000  for  the  steel  shaft  and  40,000  for  the 
wrought-iron  bolts,  and  using  a  factor  of  safety  of  5,  we  have 


It  is  evident  that  we  must  find  R  before  we  can  deter- 
mine d.  The  following  table,  by  D.  A.  Low,  gives  values  of 
d  and  n  for  solid  shafts: 


TABLE   22. 

FLANGED    SHAFT-COUPLINGS. 


D 

n 

d 

• 

d 

Z? 

» 

d 

• 

d 

3 

3 

\\ 

4 

7 
¥ 

14 

6 

3i5* 

8 

2l| 

4 

3 

4 

4 

15 

6 

3T9Tr 

8 

31* 

5 

4 

IT7^ 

6 

16 

6 

3il 

8 

31 

6 

4 

Ii:i 

6 

*T  IT 

17 

6 

4iV 

8 

7 
8 

4 
4 

2 

6 
6 

IY 

18 
19 

6 

8 

4 

8 
9 

1 

9 

6 

21 

8 

ii 

20 

8 

4A 

9 

4 

10 

6 

2| 

8 

2i 

21 

8 

4S 

9 

4A 

ii 

6 

2f 

8 

2T5<r 

22 

8 

41 

9 

41 

12 

6 

2i 

8 

2* 

23 

8 

4tt 

9 

4i9«r 

13 

6 

31 

8 

»| 

24 

8 

5TV 

9 

</,  =  diameter  of  screwed  part  of  bolt  = 
H '—  height  of  nut  — 


to 


When  the  bolts  are  i-J"  diameter  or  over  they  are  usually 
tapered,  and  tapered  bolts  are  often  made  without  heads. 
For  taper  of  bolt  use  f"  in  12".  (See  Exercise  13.) 


C  =  diameter  of  bolt  centre  =  D  +  2.25^. 


SHAFTING   AND   SHAFT-COUPLINGS.  l8l 

While  the  shearing  resistance  of  the  bolts  increases  as  the 
diameter  C  increases  with  the  same  diameter  of  bolt,  yet  to 
avoid  the  unnecessary  use  of  material  in  the  flanges,  and 
secure  a  maximum  of  tightness  in  the  coupling,  the  diameter 
C  should  be  made  as  small  as  it  is  convenient  to  make  it. 

/  =  thickness  of  flange  =  .$D\ 

F  —  diameter  of  flange  =  D  -\-  $.gd. 

e=D,-l".  f=d,. 

When  cylindrical  heads  are  used  in  tapered  bolts  their 
diameter  may  be  J"  larger  than  the  largest  diameter  of  the 
bolt,  and  the  height  equal  to  |^. 


FIG.  126. 

Jaw  Clutch  Coupling. — This  coupling,  shown  in  Figs. 
126  and  127,  is  such  that  one  half  may  be  geared  with  or  dis- 
geared  from  the  other  half  at  will,  and  for  slow-moving  shafts 
this  arrangement  is  simple  and  effective. 

Exercise  51. — Make  drawings  as  shown  in  Fig.  127  for  a 
steel  shaft  3"  diameter.  The  other  dimensions  may  be  taken 
from  Table  23. 

Spiral-jaw  Coupling.  This  form  of  coupling,  shown  in 
Figs.  128  and  129,  has  axial  engagement  and  is  the  commonest 


182 


DRAWING   AND    DESIGNING. 


SH At  TING   AND    SHAFT-COUPLINGS. 
TABLE   23. 

JAW   CLUTCH    COUPLINGS. 
(Dimensions  are  in  inches.) 


183 


3* 
31 

4* 

9 

^ 

7£ 

8f 


"i 

12} 


2t 

2| 

3t 

3! 

4 

4l 

4f 

Sir 

5: 

6 

7» 
8J 
9: 

Hi 
13 


31 

4i 

41 

5i 

5| 

71 

Sir 

ioi 


16 


6i 
6| 
7* 


i3f 
16! 


1/2 

5/8 
3/4 
7/8 
i 

!i 


2 

S 
2f 


i    13/16 

7/8 
15/16 


i/4 

3/8 

3/8 

3/8 

7/16 

7/i6 

7/i6 

7/i6 

9/16 

9/i6 

5/8 

11/16 

3/4 
13/16 


1/2 

1/2 
1/2 
1/2 
1/2 
1/2 

5/8 
5/8 
5/8 
5/8 
5/8 
3/4 
3/4 
3/4 


I3/16J  3/4 
i5/i6|  7/8 


of  its  kind.      It  is  readily  thrown  in  and  out  of  gear  by  means 
of  a  lever  and  fork  working  in  a  groove  shown  at  the  right  of 


FIG.  128. 


the  figure.     This  style  of  clutch  is  adapted  to  the  transmis- 
sion of  motion  in  one  direction  only. 


1 84 


DRAWING  AND   DESIGNING. 


SHAFTING   AND    SHAFT-COUPLINGS.  185 

Exercise  52. — Make  drawings  of  a  spiral-jaw  coupling  for 
a  2%'  shaft,  as  shown  in  Fig.  129.  Scale  6"  =  /  foot. 

The  Universal-joint  Coupling. — This  most  common  of 
flexible  couplings  is  best  known  as  Hooke's  coupling. 
Reuleaux  says :  "  If  not  the  original  inventor  of  the  Universal 
Joint,  the  Italian  Cardan  was  the  first  to  describe  it  (1501- 
1576),  and  the  Englishman  Hooke  (1635-1702)  first  applied 
it  for  the  transmission  of  rotary  motion."  The  practical 
value  of  this  form  of  coupling  is  that  it  can  be  used  to  con- 
nect two  shafts  whose  axes  intersect,  and  the  angle  between 
the  shafts  may  be  varied  during  rotation ;  this  latter  feature 
makes  it  suitable  for  ship  propeller-shafts,  to  allow  for  the 
flexure  due  to  the  elasticity  of  the  hull  of  the  vessel. 

The  coupling  shown  in  Fig.  130  is  called  a  double-joint 
coupling  because  of  the  intermediate  piece  shown  at  5,  and 
is  such  that  two  shafts  in  the  same  plane  and  making  equal 
angles  with  the  intermediate  piece  (S)  will  rotate  with 
uniform  angular  velocity.  This  coupling  is  made  by  the 
Dodge  Mfg.  Co.,  Mishawaka,  Indiana. 

Exercise  53. — Make  complete  drawings  as  shown  in  Fig. 
130.  Scale  6"  =  I  foot. 

Propeller-shaft  Coupling. — Fig.  131  shows  a  propeller- 
shaft  coupling,  designed  by  the  Campbell  &  Zell  Co., 
Baltimore,  Md.  The  material  of  the  coupling  and  coupling- 
nut  is  wrought  steel.  The  design  is  neat,  compact,  compara- 
tively inexpensive,  and  has-given  good  satisfaction. 

Exercise  54. — Make  drawings  of  Fig.  131  as  shown,"  except 
that  the  diameter  of  the  bolts  is  to  be  calculated  by  equa- 
tions (20)  and  (2 1)  (so  that  the  resistance  to  shearing  of  bolts 
will  be  equal  to  resistance  to  torsion  of  shaft  divided  by  J?), 


1 86 


DRAWING   AND   DESIGNING. 


SHAFTING  AND   SHAFT-COUPLINGS. 


.187 


188  DRAWING   AND    DESIGNING. 

and  make  the  diameter  of  the  bolt-centre  circle  and  the  outer 
diameter  of  the  coupling  to  suit.     Scale  6"  =  i  foot. 

In  equation  (20)  use  D  equal  to  the  mean  diameter  of  the 
tapered  part  of  the  shaft,  and  from  the  result  of  equation 
(21)  take  the  nearest  commercial  bolt  diameter  found  in 
Table  8. 


CHAPTER   V. 
PIPES   AND   PIPE-COUPLINGS. 

Pipes.  —  Pipes  are  made  of  cast  iron,  wrought  iron,  steel* 
copper,  and  brass,  and  used  to  convey  steam,  water,  or  gas. 
Copper  pipes  are  used  most  largely  in  marine  work,  and  brass 
pipes  or  tubes  are  used  to  some  extent  in  Europe  for  the  fire- 
tube  boilers  of  locomotives  and  for  other  purposes. 
Thickness  of  Pipes  to  Resist  Internal  Pressure. 
Let  D  =  internal  diameter  of   pipe  or  mean  diameter  for 

very  thick  pipes; 

/  =  length  of  pipe  in  inches,  inside  of  flanges  ; 
P  =  internal  pressure  in  pounds  per  square  inch  ; 
/  —  thickness  of  pipe  in  inches  ; 
ft  =  safe    tensile    stress    in    material    in    pounds   per 

square  inch. 

Then  the  total  force  tending  to  separate  two  sections  of 
the  shell  =  P  X  D  X  /,  which  is  resisted  by  the  two  thick- 
nesses of  the  shell  X  the  length  of  the  pipe  X  the  pressure 
per  square  inch,  or  2(///J);  from  this  we  get 

-  PD 


This  formula  gives  a  thickness  somewhat  less  than  is  used 
in  practice. 

189 


1 go  DRAWING   AND    DESIGNING. 

D.  A.  Low  gives 

PD 


'=-*+<• 


and  the  values  of  k  and  c  as  follows: 


TABLE  24. 


(2) 


k 

£• 

4  ooo 

Oa 

3  COQ 

O  ^ 

17  OOO 

40  ooo 

7  ooo 

4^0 

O-7 

For  foundry  reasons  cast-iron  pipes  should  never  be  less 
than  Y\"  thick,  and  long  lengths  not  less  than  ^" . 

For  tables  giving  the  thickness  of  pipes  for  various  pres- 
sures and  equivalent  heads  see  Kent's  "  Mechanical  Engineers' 
Pocket-book,"  p.  189. 


PIPE-COUPLINGS. 

Cast-iron  Pipe-couplings. — The  most  common  method 
of  connecting  cast-iron  pipes  is  by  flanges  cast  on  the  pipes 
as  shown  in  Fig.  131. 

Exercise  55. — Make  drawings  of  a  cast-iron  pipe-coupling 
like  Fig.  131.  D  =  8".  Calculate  remaining  dimensions  by 
the  following  formulae.  Scale  6"  —  i  foot. 

t  —  o.02$D  -\~  0.327; 
F=  0.033^  +  0.56; 


PIPES  At\D    PIPE-COUPLINGS.  19! 

£=  1.125/7  +  4.25; 

C  —  1.092/7  +  2.566; 

d  =  o.Oi  iD  +  0.73  ; 

n  =  number  of  bolts  —  0.78/7+  2.56; 

w  =  weight  of  pipe  per  foot  =  0.24/7*  +  3/7* 

W=       "        "  flange  =  .ooi/78  +  o.i/73  +  /7+  2. 

This  joint  has  the  flanges  faced  all  over,  and  is  used  for 
pressures  up  to  75  Ibs.  per  square  inch  (170  ft.  of- head);   for 


FIG.  131. 

higher  pressures  the  joint  may  be  made  with  a  string  smeared 
with  red  lead  between  the  flanges  or  a  lead,  india-rubber,  or 
gutta-percha  ring. 

Exercise  56 — Make  drawings  of  a  cast-iron-pipe  flange 
coupling,  Fig.  132.  Inside  diameter  of  pipe  to  be  9",  other 
dimensions  to  be  taken  from  Table  25.  Scale  6"  =  I  foot. 


I92 


DRAWING   AND    DESIGNING. 


TABLE   25. 

STANDARD    CAST-IRON    FLANGES. 
(.Dimensions  are  in  inches.) 


Stress  on 
Each  Bolt  per 

Stress  on 

D 

* 

n 

C 

F 

£ 

d 

Sq.  Inch  at 
Bottom  of 

/ 

Pipe  per 
Sq.  Inch  at 

Thread  at 
200  Lbs. 

200  Lt  s. 
Pressure. 

2 

.409 

4 

4! 

5/8 

6 

5/8 

825 

i/4 

460 

2k 

.429 

4 

5i 

11/16 

7 

5/8 

1050 

i/4 

550 

3 

.448 

4 

6 

3/4 

7* 

5/8 

1330 

i/4 

690 

3i 

.466 

4 

6| 

13/16 

8-i 

5/8 

2530 

5/i6 

7OO 

4 

.486 

4 

7* 

15/16 

9 

3/4 

2IOO 

5/i6 

800 

4? 

.498 

8 

7! 

15/16 

91 

3/4 

1430 

5/i6 

900 

5 

.525 

8 

si 

15/16 

10 

3/4 

1630 

3/8 

1000 

6 

.563 

8 

9l 

i 

ii 

3/4 

2360 

3/8 

ic6o 

7 

.60 

8 

lOf 

** 

121 

3/4 

3200 

3/8 

1  1  20 

8 

639 

8 

ii? 

'i 

I3i 

3/4 

4190 

3/8 

1280 

9 

.678 

12 

13 

ij 

15 

3/4 

36lO 

3/8 

1310 

10 

•  713 

12 

i4i 

i  A 

16 

7/8 

2970 

3/8 

1330 

12 

•79 

12 

16} 

i| 

19 

7/8 

4280 

3/8 

1470 

This  table  was  adopted  by  a  conference  of  committees  of  the  A.S.M.E. 
and  the  Master  Steam  and  Hot  Water  Fitters  Association  in  July,  1894. 
Sizes  up  to  24"  diameter  are  designed  for  200  Ibs.  pressure  per  square  inch 
or  less. 


PIPES    AND   PIPE-COUPLINGS. 


'93 


Spigot-and-socket  Joint. — This  is  the  usual  joint  for 
pipes  that  have  to  be  embedded  in  the  earth  for  conveying 
water  or  gas.  Fig.  143  shows  a  joint  of  this  kind.  About 
half  of  the  space  between  the  spigot  and  socket  is  first  filled 
with  rope  gasket  and  into  the  remaining  half  is  poured  molten 
lead,  which  when  it  cools  is  calked  tightly  into  the  socket 
with  a  hammer  and  round-nos^H  tool. 


FIG.  133. 

Exercise  56. — Make  drawings  of  a  spigot-and-socket  coup- 
ling for  an  8"  cast-iron  pipe  carrying  a  pressure  of  100  Ibs. 
per  square  inch  (Fig.  133).  Scale  6"  =  i  foot. 

Same  elevations  and  sections  as  in  Ex.  55.  Calculate  the 
dimensions  from  the  following  proportions: 

D  =  internal  diameter  of  pipe; 

PD 
t  =  thickness  of  pipe  =  — -  +  c  from  equation  (2) ; 


I94 


DRA  WING   AND    DESIGNING. 


=  .075^  + 


/=  .045/7  +.8; 

.F=:    .04/7+   .7 

Exercise  57.  —  Make  working  drawings  for  the  spigot-and- 
socket  cast-iron  pipe-coupling  shown  in  Fig.  134.  Internal 
diameter  of  pipe  10".  Elevations  and  sections  similar  to 
Ex.  55.  Scale  6"  =  i  foot. 


FIG.  134. 

The  dimensions  for  this  problem  are  to  be  calculated  from 
the  proportions  given  for  Ex.  56.  The  turned  and  fitted 
part  E  is  made  with  a  taper  of  I"  in  12" . 

Exercise  58. — Make  working  drawings  of  an  8"  cast-iron- 
pipe  flange  coupling  like  Fig.  135.  Elevations  and  sections 
as  in  Ex.  55.  Scale  6"  —  I  foot. 

Dimensio'ns  to  be  taken  from  Table  25. 


PIPES  AND   PIPE-COUPLINGS. 


'95 


These  pipe-ends  and  flanges  are  strengthened  with   ribs 
drawn  at  an   angle  of  45°  with  the  axis  of  the  pipe,  and  the 


joint  is  made  by  means  of  fitting- strips  cast  on  the  flanges 
equal  in  width  to  the  thickness  of  the  pipe.  The  faces  of 
these  strips  are  finished  perfectly  square  with  the  axes  of  the 
pipes,  and  before  bolting  up  are  smeared  with  red  lead. 

Exercise  59. — Make  drawings  of  the  loose  flange  coupling 
for  a  copper  pipe  shown  in  Fig.  136.  Inside  diameter  of 
pipe  8".  Scale  6"  =  i  foot. 

This  joint  is  the  invention  of  Mr.  R.  B.  Pope  of  Dumbar- 


FIG.  136. 


196 


DRAWING   AND    DESIGNING. 


ton,  Scotland,  and  is  given  by  Low  and  Bevis.  The  flange 
rings  may  be  made  of  cast  iron,  wrought  iron,  wrought  steel, 
or  cast  steel;  the  latter  is  preferred.  It  is  evident  from 
Fig.  136  that  the  rings  must  be  placed  on  the  pipes  before 
the  ends  are  flanged. 

These  joints  have  been  used  for  steam-,  feed-,  and 
exhaust-pipes  from  ij"  to  36"  diameter. 

The  dimensions  may  be  taken  from  the  following  table: 


TABLE  26. 

POPE'S    PIPE   COUPLINGS. 
(Dimensions  are  in  inches.) 


D 

A 

B 

c 

d 

No.  of 
Bolts. 

D 

A 

B 

C 

d 

No.  of 
Bolts. 

H 

7/8 

7/8 

4 

3/4 

5 

4) 

15/16 

irV 

7$ 

7/8 

8 

•2 

7/8 

15/16 

4^ 

3/4 

5 

5 

I 

«* 

8 

i 

8 

2j 

7/8 

I5/I6 

5i 

3/4 

6 

6 

I 

ifV 

9^ 

i 

9 

3 

15/16 

i 

5! 

7/8 

6 

7 

ITV 

ri 

.10* 

tl 

9 

3i 

ic/i6 

i 

6i 

7/8 

6 

8 

iTV 

i 

ui 

*! 

10 

4 

15/16 

*A 

6| 

7/8 

7 

9 

iiV 

IT5* 

12* 

«l 

10 

Wrought-iron  and  Steel  Pipe-couplings.  —  Fig.  137 
shows  a  very  efficient  form  of  joint  for  wrought-iron  pipes. 
The  flanged  ends  of  the  pipes  are  countersunk  into  the  cast 
flange  rings,  and  the  bolt-heads  are  also  countersunk  about  f 
of  an  inch.  Between  the  flanged  ends  of  the  pipes  is  placed 
a  ring  of  lead  •§•"  thick  and  from  f/x  to  f"  wide. 

Exercise  60. — Make  drawings  of  the  joint  shown  in  Fig. 
137  for  a  6"  wrought-iron  pipe.  Scale  full  size. 

A  should  be  made  equal  to  i.2$d.  t  may  be  taken  from 
Table  7.  Remaining  dimensions  ma}7  be  taken  from  Table  26. 


PIPES  AND    PIPE-COUPLINGS. 


197 


FIG.  137. 

The  "  Converse"  joint  for  wrought-iron  and  steel  pipes  is 
shown  at  Fig.  138.  It  is  manufactured  by  the  National  Tube 
Works,  McKeesport,  Pa.  This  joint  consists  of  a  cast-iron 
sleeve  with  a  space  for  lead  at  each  end ;  there  are  also 
internal  recesses  plainly  shown  in  Fig.  138,  into  which  are 


FIG.  138. 


inserted  rivet-heads  on  the  ends  of  the  pipes,  and  by  a  turn 
of  the  pipes  the  flanges  become  locked  in  position.  Molten 
lead  is  poured  into  these  recesses  around  the  rivet-heads  and 
tightly  calked  at  the  ends  of  the  sleeves,  as  shown  in  Fig.  139. 


198 


DRAWING   AND   DESIGNING. 


Exercise  61. — Make  drawings  of  the  Converse  joint  for  a 
7"  wrought-iron  pipe,  according  to  the  dimensions  given  in 
Fig-  !39-  Elevations  and  cross-sections  same  as  in  Ex.  55. 
Scale  6"  =  i  foot. 


FIG.  139. 

Screwed  -  flange  Pipe -coupling.  —  Fig.  140  shows  a 
wrought-iron  pipe-joint  made  by  screwing  cast-iron  flanges 
on  the  ends  of  the  pipes  and  held  together  by  bolts.  It 
is  used  by  the  Philadelphia  &  Reading  Coal  and  Iron  Co.  for 
their  steam-pipes.  The  threads  of  the  screws  on  the  pipes 
are  made  according  to  the  Briggs  standard.  The  lugs  shown 
in  the  figure  on  the  right-hand  flange  are  cast  on,  and  have 
their  inner  surfaces  finished  to  fit  the  cylindrical  fitting-piece 
on  the  other  flange.  The  ring  shown  between  the  flanges  is 
of  gum  rubber  and  makes  the  joint  steam-tight.  The  pipes 
are  made  in  lengths  of  from  16  to  20  ft. 

Exercise  62. — Draw  a  screwed-flange  pipe-coupling  like 
Fig.  140  for  an  8"  wrought-iron  pipe.  Scale  6"  =  i  foot. 

Dimensions  may  be  taken  from  the  following  table : 


PIPES  AND   PIPE-COUPLINGS. 


I99 


200 


DRAWING   AND   DESIGNING. 


TABLE  27. 

STEAM-PIPE   CONNECTIONS   OF    PHILA.    &    READING   COAL  AND    IRON   CO. 
(Dimensions  are  in  inches.) 


D 

f 

A 

B 

c 

E 

No.  of 
Bolts. 

d 

F 

G 

a 

No.  of 
Lugs. 

/ 

3 

.217 

5 

1/2 

6 

7t 

4 

3/4 

3/4 

1/2 

7/8 

4 

3/4 

3* 

.226 

5i 

1/2 

6| 

8* 

4 

3/4 

3/4 

1/2 

7/8 

4 

3/4 

4 

.237 

6 

1/2 

7£ 

9i 

4 

7/8 

7/8 

1/2 

7/8 

4 

3/4 

5 

.2^9 

7 

1/2 

84 

10* 

4 

7/8 

7/8 

1/2 

7/8 

4 

3/4 

6 

.280 

8 

1/2 

10 

12 

6 

7/8 

i 

1/2 

7/8 

4 

3/4 

7 

.301 

9 

I/a 

ii 

13 

6 

7/8 

i 

1/2 

7/8 

4 

3/4 

8 

.322 

10 

5/3 

12 

M 

6 

7/8 

ii 

1/2 

7/8 

6 

i 

9 

.322 

ii 

5/8 

13 

15 

8 

i 

ii 

1/2 

7/8 

6 

i 

10 

.366 

12 

5/8 

14 

i6i 

8 

i 

ii 

1/2 

7/8 

6 

i 

Screwed-socket  Coupling — Fig.  141  shows  a  screwed- 
socket  coupling  for  a  wrought-iron  pipe.  The  socket  is 
screwed  half-way  on  to  the  end  of  one  pipe,  and  the  other 
pipe  is  then  screwed  into  the  remaining  half  of  the  socket. 
When  it  is  not  feasible  to  screw  the  long  lengths  of  pipe  into 
the  projecting  end  of  the  socket,  a  screw  is  cut  on  one 
length  of  pipe  and  the  socket  is  screwed  fully  on  to  this 
length,  and  when  the  pipes  are  butted  together  the  socket  is 
screwed  back  until  it  is  half  on  each  pipe. 

For  other  wrought-iron  or  steel  pipe-connections,  see 
samples  in  drafting-rooms. 

Exercise  63. — Make  drawings  of  a  wrought-iron  socket 
pipe-coupling  fj"  nominal  diameter,  to  dimensions  given  in 
Fig.  141.  Elevations  and  sections  same  as  Ex.  55.  Scale 
full  size. 

Locomotive  Steam-pipe  Ball  Joint. — This  joint  (Fig. 
142)  is  made  between  the  steam  branch  pipe  (a)  and  the  tee- 


PIPES  AND    PIPE-COUPLINGS. 


201 


pipe  (b)  which  conducts  the  steam  from  the  dome  and  dry- 
pipe  to  the  steam-chests  of  the  cylinders  on  each  side  of  the 
engine.  The  pipes  are  of  cast  iron,  and  the  spherical  joint-ring 


is  of  brass.  The  ball  joint  allows  for  expansion  and  contrac- 
tion and  for  the  pipe  to  be  set  at  various  angles  with  the 
perpendicular  and  horizontal. 


202 


DRAWING   AND   DESIGNING. 


Exercise  64. — Make  drawings,  as  shown  by  Fig.  142,  of  a 
locomotive  steam-pipe  ball  joint  to  dimensions  given.  Scale 
6"  =  i  foot. 


PIPES  AND   PIPE-COUPLINGS. 


2O3 


Wrought-iron  Flange  Pipe-coupling. — Fig.  143  shows 
a  pipe-coupling  made  with  angle-iron  for  a  steel  pipe.  The 
angle-iron  is  rolled  and  welded  into  rings  and  riveted  to  the 
pipes.  These  flanges  are  used  for  either  wrought-iron  or 


FIG.  143- 

steel   pipes.     The  joint   is  made  steam-tight  by  means  of  a 
lead  ring  inserted  between  the  flanges  as  shown. 

Exercise  65. — Make  drawings  of  a  steel  pipe  with  wrought 
iron  flange  coupling  like  Fig.  143.  Nominal  size  of  pipe  8" 
diameter.  Elevations  and  sections  like  Ex.  55.  Scale  6"  =  I 
foot. 

Couplings  for  Brass  and  Copper  Pipes. — The  coupling 
shown  in  Fig.  144  is  used  on  locomotive-boiler  feed-pipes, 
injector-pipes,  etc.  The  sleeves  (a)  and  (b)  are  brazed  to  the 
pipes,  and  a  thin  copper  gasket  placed  between  the  ends  of 
the  sleeves  makes  the  joint  thoroughly  tight  when  screwed 
up  with  the  fluted  nut  (c). 

Exercise  66. — Make  drawings,  as  shown  in  Fig.  144,  of  a 
brass  pipe-coupling,  outside  diameter  to  be  2j" '.  Scale  full 
size. 

The  dimensions  may  be  taken  from  Table  28. 


204 


DRA  WING  AND    DESIGNING. 


a 


TABLE   28. 

COUPLINGS    FOR    BRASS,    COPPER,    AND    WROUGHT-IRON    PIPES. 
(Dimensions  are  in  inches.) 


d 

.4 

B 

C 

D 

E 

^~ 

e 

H 

/ 

K 

L 

M 

/ 

I* 

i* 

it 

Jft 

ifl 

I 
I 

I 

5/i6 
3/8 
3/8 

lit 

2Y 
2T5ff 

\\ 
l| 
2 

2 

3 

3/4 
3/4 
3/4 

I 
I 

2i 
2f 

2f 

3/8 
3/8 
3/8 

5/8 
5/8 
5/8 

2I 
2il 
3f* 

i 

2 

2T8* 

Ii 

3/8 

2« 

2i 

3 

7/8 

Ii 

3f 

7/16 

3/4 

^ 

2i 

H 

a 

Ii 
Ii 

7/i6 

1/2 

3Y 
3T6ff 

2J 

2| 

1! 

7/8 
7/8 

Ii 

Ii 

1! 

7/16 
7/16 

3/4 
3/4 

4^ 
il 

PIPES  AND   PIPE-COUPLINGS. 


205 


TABLE  29. 


FORM  OF  SECTION 


AREA 
OFSECTION 


MODULUS  OF 
SECTION  Z. 


FORM  OF  SECTION 


MODULUS  OF 
SECTION  Z. 


:_i_ 


*'-. 

7854  d 


0982d,3. 


7854AB0982BA2 
bd 


b2 


b 


/\     ; 

JT 

A  i 


b(b-d) 


6 


.118b 


6    D 


CHAPTEE   VI. 
BEARINGS,   SOLE-PLATES,   AND   WALL   BOX-FRAMES. 

ALL  pieces  employed  in  the  transmission  of  power,  rotating 
about  a  geometrical  axis,  must  be  supported  in  such  a  manner 
as  to  allow  free  rotation.  The  supports  receive  the  general 
name  of  bearings,  the  various  types  being  designated  accord- 
ing to  the  direction  of  the  pressure  acting  upon  them.  When 
the  pressure  is  perpendicular  to  the  axis  of  the  shaft  they  are 
journal-bearings,  and  when  bearings  of  this  type  and  the  frame- 
work connected  with  them  are  independent  parts  of  a  machine, 
they  are  indiscriminately  called  Plummer  Blocks,  Pillow 
Blocks,  or  Pedestals. 

When  the  pressure  is  parallel  to  the  axis  of  the  shaft  and 
the  shaft  terminates  at  the  bearing  surface,  Fig.  164,  the  bear- 
ing is  a  pivot-bearing.  When  this  type  of  bearing  is  employed 
for  supporting  the  weight  of  a  vertical  shaft,  it  is  termed  a 
step-  or  footstep-bearing.  When  the  pressure  is  parallel  to 
the  axis  of  the  shaft  and  the  shaft  is  continued  through  the 
bearing,  the  latter  is  termed  a  collar-bearing. 

When    pivot-   or    collar-bearings    are    used     on   horizontal 
shafts  they  are  called  thrust-bearings. 

Journals  are  the  parts  of  the  shafts  or  axles  that  revolve 
on  the  bearings.  They  are  made  cylindrical,  conical,  or 
spherical,  of  which  the  cylindrical  is  the  most  common  form. 

206 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  2O7 

To  limit  the  longitudinal  motion  of  journals  the  shafts  are 
turned  down  or  have  collars  forged  upon  them  to  form 
shoulders  which  come  in  contact  with  the  faces  of  the  bear- 
ings upon  which  the  journals  revolve.  When  practicable  the 
length  of  journals  should  be  about  one  per  cent  greater  than 
that  of  their  bearings. 

The  Area  of  a  Bearing  is  the  width  of  the  chord  of 
the  arc  in  contact  with  the  journal,  multiplied  by  the 
length  of  the  bearing.  This  is  sometimes  called  the  projected 
area,  because  it  is  the  area  of  the  contact  surface  projected 
on  to  a  plane  perpendicular  to  the  direction  of  the  pres- 
sure. Thus  the  area  of  a  cylindrical  journal-bearing,  Fig. 
164,  is  D  X  L.  The  area  of  a  pivot-bearing,  Fig.  278,  is 

— .     The  area  of  a  collar-bearing  is  -  (D*  -  D?)N.    Where 

4  4 

D  is  the  diameter  of  the  shaft  Z>,  is  the  outside  diameter  of 
collars  and  N  the  number  of  collars. 

Solid  Journal-bearings. — The  simplest  form  of  journal- 
bearing  is  made  by  drilling  a  hole  through  the  frame  of  the 
machine,  and  to  provide  sufficient  bearing  surface  the  length 
of  the  bearing  is  increased  by  casting  projections,  which  are 
termed  bosses,  upon  the  frame,  as  in  Fig.  145.  In  this  form 
of  bearing  there  is  no  provision  for  wear,  and  the  shaft  can 
be  returned  to  its  initial  position  only  by  renewing  that  part 
of  the  frame  that  carries  the  shaft,  or,  when  the  hole  wears 
oval,  reboring  the  bearing  sufficiently  to  fit  it  with  a  cylindri- 
cal sleeve  or  bush,  as  in  Fig.  146.  Such  a  bearing  may  be 
provided  with  a  bush  or  lined  with  soft  metal,  and  can 
be  restored  to  its  original  condition  by  renewing  the  bush  or 
lining.  The  end  movement  of  the  shaft  may  be  limited 


208 


DRAWING   AND    DESIGNING. 


by  making  the  diameter  of  one  of  the  journals  less  than  the 

diameter  of  the  shaft,  thereby 
forming  a  shoulder  which  limits 
the  end  movement  in  one  direc- 
tion, and  securing  a  separate 
collar  to  the  shaft,  by  means 
of  a  set-screw  or  taper-pin,  in 
such  a  position  as  to  limit  the 
end  movement  in  the  other 
direction,  as  shown  in  Fig.  145. 
Another  method  is  to  make 
the  shaft  of  uniform  section 
throughout  its  length,  limiting 
its  end  motion  by  means  of 
two  separate  collars  which  may 
be  arrapged  in  three  different 
positions. 

Exercise  67.  —  Draw  two 
solid  journal-bearings  support- 
ing  a  shaft  2"  in  diameter,  mak- 
ing the  area  of  the  bearing  sur- 
face 6  square  inches,  and  show 
an  arrangement  for  limiting  the 
end  movement  in  either  direc- 
tion by  means  of  one  loose 
collar,  as  shown  in  Fig.  145. 
Draw  also  one  bearing  if"  in 
diameter  with  a  brass  bush  or 
sleeve,  as  shown  in  Fig.  146. 

Make  /  equal  to  o.i</+    *  ".      Parts  dimensioned   in  decimal 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.   2OQ 

fractions  are   proportional  to  d.     Complete   and   fill   in   the 
actual  dimensions  to  the  nearest  sixteenth.     Scale  full  size. 

As  the  shafts  supported  by  solid  journal-bearings  cast  with 
the  machine-frame  have  to  pass  through  one  bearing  to  the 
other,  this  form  of  bearing  cannot  be  used  when  there  are 
projections  on  the  shaft.  A  solid  bearing  can  be  used,  how- 
ever, for  supporting  a  shaft  upon  which  there  are  projections,  * 
by  making  the  bearings  independent  parts  and  securing  them* 
to  the  machine-frame  by  means  of  bolts.  By  this  arrange- 
ment the  shaft  is  turned  down  on  the  ends  to  form  the 
journals,  and  one  of  the  bearings  is  placed  on  its  journal 
before  it  is  secured  to  the  frame.  This  form  of  bearing, 
Fig.  147,  consists  of  a  hollow  cylinder  cast  upon  a  base 
through  which  bolts  are  passed  into  the  machine-frame  or 
supporting  bracket. 

Fig.  147  shows  a  design  of  a  solid  journal-bearing  used  for 
supporting  the  valve-gear  reversing-shaft  of  a  locomotive. 
Such  a  bearing  can  be  used  for  this  purpose  because  it  is 
subjected  to  a  comparatively  light  load,  while  the  journal  has 
•a.  slow  and  intermittent  movement.  The  length  and  shape 
of  the  bearing  in  this  design  are  determined  by  local  condi- 
tions, the  bearing  being  carried  forward  further  on  one  side 
of  the  base  than  on  the  other  to  suit  the  shaft.  The  width 
of  the  base  is  determined  by  the  thickness  of  the  frame, 
and  is  provided  with  strips  on  the  under  side  to  facilitate 
iitting. 

Exercise  68 — Draw  an  elevation  and  plan  of  a  solid 
journal-bearing  of  the  form  shown  in  Fig.  147,  making  d  = 
2^"  and  L  =  2d.  The  parts  dimensioned  in  decimal  fractions' 
are  proportional  to  d.  Scale  full  size. 


210 


DRAWING   AND    DESIGNING. 


Construction. — First  draw  the  centre  lines  and  complete 
the  cylindrical  part  of  the  bearing.  Make  the  distance  a 
equal  to  the  outside  radius  of  the  cylindrical  part  -f-  r,  the 


FIG.  147. 

radius  of  the  fillet,  which  we  will  make  equal  to,  say,  •§•"  -f- 
half  the  distance  across  the  angles  of  the  nut  -f-  \"  for  clear- 
ance. The  distance  b  can  be  made  equal  to  half  the  distance 
across  the  angles  of  the  nut  +  £''. 

Divided  Bearings. — Where  the  conditions  are  such  that 
the  shaft  cannot  be  placed  upon  its  bearings  endwise,  the 
bearings  are  parted  and  the  parts  fastened  together  by  means 
of  bolts  or  screws.  The  division  is  generally  made  on  the 
line  normal  to  the  resultant  pressures  on  the  bearing. 


BEARINGS.  SOLE-PLATES,  AND    WALL   BOX-FRAMES.   211 

In  Fig.  148  is  shown  what  is  generally  termed  a  two-part 
bearing.  It  consists  of  the  block  P,  upon  which  the  journal 
is  supported,  and  the  cap  C,  which  is  secured  to  the  block  by 
the  bolts  CB.  In  this  design  the  journal  is  intended  to  be 
lubricated  with  semi-liquid  grease  which  is  passed  through 
the  opening  O.  The  bearing  is  lined  with  Babbitt  metal, 
.oSD  +  TV"  thick.  The  holes  through  which  the  holding- 
down  bolts  pass  are  made  oblong  to  horizontally  adjust  the 
pedestal. 

Wall  Box-frames  are  built  into  the  wall  for  the  purpose 
of  supporting  a  bearing  for  shafting  which  passes  from  one 
room  or  building  to  another.  Fig.  149  shows  a  wall  box- 
frame  with  an  arched  top  to  support  the  wall  above  it.  On 


FIG.  149. 

the  sides  are  cast  projecting  webs  W  which  fit  into  the  wall  to 
keep  the  frame  from  moving  endwise.  The  upper  side  of  the 
base  is  provided  with  raised  machined  strips  FS  upon  which 
the  pedestal  rests,  as  shown  in  Fig.  150,  and  at  each  end  of  this 
surface  are  projections  5,  on  the  sides  of  the  frame,  which 
are  also  machined.  To  adjust  the  pedestal  horizontally, 
wooden  keys  of  the  necessary  thickness  are  fitted  between 
the  surface  S  and  the  pedestal  base.  The  height  H  is  equal 


212 


DRAWING  AND   DESIGNING. 


to  the  highest  point  of  the  pedestal  cap  when  raised  clear  of 
the  cap-bolts  CB  +  about  6"  to  allow  the  engineer  to  remove 
the  cap.  The  length  ^  is  equal  to  /,  the  length  of  the  base,  + 
the  amount  of  horizontal  adjustment  allowed  on  the  pedestal 


•iff 

4  w   I     t 


D.R, 


FIG.  150. 


+  i".  The  width  «/  is  made  to  suit  the  thickness  of  the 
wall,  which  is  usually  built  to  average  from  8"  to  12" .  The 
proportioning  of  such  a  piece  is  largely  a  matter  of  experi- 
ence, none  of  the  parts  being  calculated  for  strength. 

Exercise  69. — Draw  a  pedestal  and  wall  box-frame  of  the 
designs  shown  in  Figs.  148  and  150,  placing  the  pedestal  in 
position  on  the  wall  box-frame,  to  which  it  is  secured  by  two 
square-headed  bolts  the  heads  of  which  project  below  the 
base.  Make  the  pedestal  to  suit  a  shaft  2%'  in  diameter,  the 
length  L  equal  to  3/?,  and  the  width  ?u  of  the  frame  equal  to 
8".  Show  a  half-elevation  and  half-sectional  elevation  of 
the  pedestal,  and  an  elevation  of  the  wall  box-frame,  also  a 
plan  view  of  the  pedestal  with  half  of  the  cap  removed,  and 
in  combination  with  this  view  show  a  section  of  the  wall  box- 
frame  at  the  line  AB.  Make  also  an  end  view  of  the  pedestal 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  213 

and  a  sectional  end  view  of  the  wall  box-frame.  All  parts  of 
the  pedestal  are  proportional  to  the  diameter  D  of  the  journal. 
Fill  in  all  dimensions  omitted.  Scale  full  size. 

Construction. — Draw  the  vertical  and  horizontal  centre 
lines  of  the  journal,  then  determine  the  distances  from  centre 
to  centre  of  the  bolts  by  drawing  the  line  I  which  represents 
the  top  of  the  cap-flange,  and  the  arc  2,  which  represents  the 
top  of  the  cap  at  the  centre  of  the  bearing.  The  centres  of 
the  cap-bolts  can  now  be  determined  by  making  the  corners 
of  the  nuts  from  -fa"  to  \"  clear  of  the  fillet  which  joins  the 
lines  I  and  2.  It  is  obvious  that  the  bolts  may  be  brought 
nearer  together  by  either  increasing  the  thickness  of  the  cap- 
flange  or  cutting  out  the  curve  2  around  the  nut,  but  on  small 
pedestals  for  line  shafting  this  is  unnecessary.  The  radius  r 
is  made  equal  to  half  the  distance  across  the  angles  of  the  nut 
+  i"  for  finish.  The  distance  from  centre  to  centre  of  the 
holding-down  bolts  is  equal  to  the  distance  b  -\-  the  horizon- 
tal adjustment  (equal  to  the  length  of  the  hole  —  diameter  of 
bolt)  +  the  diameter  of  the  washer  +  the  radii  of  the  fillets, 
which  may  be  made  equal  to  about  J".  Determine  the 
radius  r  of  the  arched  top  of  the  wall  box-frame  by  making 

e 

V,  the  versed  sine  of  the  arc,  equal  to  — . 

4 

Half  the  elevation  is  sectioned,  to  show  more  clearly  the 
method  employed  to  keep  the  Babbitt  lining  from  turning 
with  the  shaft,  the  form  of  head  on  the  cap-bolts,  and  also 
that  the  diameter  of  the  holes  through  which  the  cap-bolts 
pass  is  greater  than  the  bolt  diameter.  The  plan  view  is 
shown  with  the  cover  removed  from  one  side  of  the  bearing, 
to  show  the  form  of  that  part  of  the  bearing  through  which 


2I4 


DRAWING   AND   DESIGNING. 


the  shaft  passes.  The  fitting-strips  on  the  under  side  of  the 
base  are  of  the  same  proportions  as  in  the  previous  exercise. 
When  practicable  it  is  usual  to  provide  the  piece  to  which 
the  bearing  is  fastened  with  fitting-strips  also,  as  in  Fig.  150. 
Post  Bearings. — When  the  bearing  has  to  be  secured  to 
a  vertical  surface,  the  base  is  cast  on  the  side,  as  shown  in 
Fig.  151.  In  the  design  shown  in  Fig.  152  it  is  necessary  to 
provide  the  cap  with  four  bolts  because  of  the  webs  W,  which 
are  in  the  way  of  the  bolts  being  placed  on  the  centre  as 
in  Fig.  148.  The  bearing  is  arranged  in  this  case  for  two 
grease-cups,  which  are  screwed  on  to  the  cap  at  the  tapped 
holes  O.  The  cap-bolts  are  kept  from  turning  when  the  nuts 
are  being  screwed  down  by  projections  h  cast  on  the  under 
side  of  the  box. 

Exercise  70. — Draw  the  elevation  and  an  end  view  half  in 
section,  as  shown  in  Fig.  152.     Draw  also  a  plan  view  of  the 

top  projected  from  the  elevation. 
Make  D  =  2f '-,  and  L  =  three  times 
D.  Parts  not  dimensioned  are  in 
the  same  proportion  to  D  as  in  the 
preceding  exercise.  Scale  half  size. 
Construction. — Draw  the  centre 
lines  of  the  bearing,  taking  care  to 
leave  sufficient  space  to  draw  the 
plan.  Mark  off  the  distance  that 
the  bearing  projects  from  the  post, 
then  determine  the  length  and  width 
FIG.  151.  of  the  base.  The  centres  of  the 

bolts  PB  should  be  in  a  distance  at  least  equal  to  the  radius 
of  the  washer  +  i"  from  the  ends  of  the  base. 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  21$ 
FIG.  148. 


2l6 


DRAWING   AND   DESIGNING. 


The  vertical  adjustment  a  is  made  equal  to  ij".  As  the 
oblong  holes  are  cored,  the  width  e  is  \"  greater  than  the 
diameter  of  the  bolts. 

Wall  Brackets  are  employed  to  carry  pedestals  which 
support  a  horizontal  shaft  running  parallel  and  near  to  a  wall. 
The  bracket,  Fig.  153,  is  fastened  to  the  wall  by  means  of 
three  bolts  which  pass  through  it  and  the  wall.  The  pedestal 


BOLTS. 


FIG.  153. 

is  secured  to  the  upper  surface  by  square-  or  T-headed  bolts 
which  slide  in  the  1  -shaped  slot  5  which  runs  the  whole 
length  of  the  bracket.  By  this  arrangement  the  distance  that 
the  pedestal  is  from  the  wall  can  be  adjusted. 

Exercise  71. — Draw  a  wall  bracket  to  the  proportions  given 
in  Fig.  153.  Make  the  slot  5  suitable  for  a  $"  square-headed 
bolt.  Draw  also  a  section,  the  plane  of  section  passing 
through  the  bracket  at  the  line  AB.  Scale  half  size. 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  2 1/ 

SELF-ADJUSTING    BEARINGS. 

Bearings  for  supporting  line  shafting  may  be  divided  into 
two  classes,  Rigid  and  Self-adjusting.  When  shafting  is 
supported  upon  a  number  of  rigid  bearings  it  is  essential  that 
they  all  be  in  line,  one  with  another,  in  order  that  the  pres- 
sure be  distributed  over  the  entire  surface  of  each.  This  is 
possible  with  bearings  of  the  "  rigid  form  "  having  compara- 
tively long  boxes  when  they  are  rigidly  supported,  but  when 
supported  upon  insecure  foundations,  which  are  liable  to  sink, 
the  bearing  will  assume  such  a  position  in  relation  to  its 
journal  as  is  shown  in  Fig.  154,  where  the  entire  load  is  carried 


DR. 


FIG.  15.1. 

upon  a  small  portion  of  the  bearing.  .Such  a  condition  exists 
also  where  the  distance  between  the  bearings  is  great  in  com- 
parison with  the  shaft  diameter,  owing  to  the  lateral  deflection 
of  the  shaft  by  the  gearing.  Under  such  conditions  the  oil  is 
forced  out  from  between  the  rubbing  surfaces,  causing  the 
metals  to  heat  and  seize  by  metallic  contact. 

To  avoid  this  localization  of  pressure,  bearings  with  a 
ball-and-socket  joint  are  used,  which  to  a  limited  extent 
adjust  themselves  to  the  various  positions  of  the  shaft,  so  that 


21 8  DRAWING  AND   DESIGNING. 

the  axis  of  the  bearing  will  always  coincide  with  that  of  the 
journal. 

This  form  of  bearing  makes  it  practical  to  use  a  long  box, 
thus  keeping  the  pressure  between  the  journal  and  bearing 
light  enough  to  retain  an  unbroken  film  of  lubricant  between 
the  rubbing  surfaces.  With  these  conditions  the  boxes  may 
be  made  of  cast-iron,  which  is  the  cheapest  and,  if  well  lubri- 
cated, the  most  desirable  metal  for  the  purpose.  Many 
engineers,  however,  prefer  to  line  these  boxes  with  a  white 
metal  which  rapidly  wears  and  adjusts  itself  to  any  irregulari- 
ties on  the  journal,  making  a  perfect  bearing  more  rapidly 
than  would  be  the  case  with  a  harder  material.  Again,  with 
the  cast-iron  box,  should  the  lubricant  fail  and  the  metals 
come  in  contact,  they  will  adhere  and  destroy  the  journal, 
while,  under  the  same  conditions,  the  babbitt  metal  would 
melt  without  materially  injuring  the  shaft. 

Drop  Hanger-frame. — When  a  shaft  is  supported  over- 
head and  is  not  near  a  wall  the  bearings  are  carried  upon  a 
frame,  called  a  hanger  frame,  which  is  secured  to  the  ceiling 
girders.  Two  forms  are  used,  the  U  form,  which  braces  the 
bearing  on  both  sides,  as  shown  in  Fig.  155,  and  the  J,  which 
braces  one  side  only. 

The  objection  to  the  U  form  as  commonly  made  is  the 
difficulty  in  getting  the  shafts  in  and  out  of  the  hanger. 
This  has  been  overcome  to  some  extent  by  making  the 
hangers  open  at  the  bottom  of  the  U,  as  it  were,  and  connect- 
ing the  sides  with  bolts. 

The  J  form  has  the  advantage  of  facilitating  the  mounting 
and  dismounting  of  the  shaft,  but  is  liable  to  vibrate  unless 
made  comparatively  heavy. 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.   21$ 

Fig.  156  shows  a  hanger  made  by  the  Dodge  Manufac- 
turing Co.  which  combines  the  advantages  of  both  forms. 
This  is  attained  by  making  the  hanger  open  on  one  side  and 
providing  it  with  detachable  links  L,  "  which  are  split,  and  by 
bolts  LJ5,  drawn  together  upon  taper  cones  C,  cast  on  the 


FIG.  155. 

hanger  frames  F,  which  match  corresponding  recesses  in  the 
parts  of  the  links.  These  links  are  thus  drawn  up  to  a  positive 
bearing  and  form  a  connection  which  is  virtually  solid,  and  yet 
they  are  easily  removed  and  replaced."  Fig.  156  shows  a  shaft 
hanger  with  an  adjustable  bearing  B<  which  is  carried  between 
the  adjusting  screws  P  and  P' ,  called  the  plungers.  These 
plungers  are  screwed  into  the  frame  F  and  serve  a  double  pur- 
pose; first,  they  are  a  means  of  obtaining  a  vertical  adjust- 


220 


DRAWING   AND   DESIGNING. 


ment ;  second,  they  provide  the  sockets,  with  which  the 
spherical  surfaces  on  the  box  engage,  to  form  the  ball-and- 
socket  joint.  The  plungers  are  locked  in  position  by  the  set- 
screws  5.  The  bearings  are  lubricated  by  filling  the  cups 


UR. 
\ 

FIG.  156. 

O  and  O'  with  grease,  or  cotton  saturated  with  oil.  The 
drippings  of  waste  oil  from  the  box  are  caught  in  the  oil  dish 
OD  attached  to  the  frame  by  hooking  the  head  over  the  pin 
P,  which  is  cast  on  the  frame. 

Exercise  72. — Draw  the  front  and  end  elevations  partly  in 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.    221 

section,  as  shown  in  Fig.  156,  a  half  plan  and  a  half-sectional 
plan  of  the  side  to  the  right,  the  plane  of  section  passing 
through  the  hanger  at  the  centre  line.  Scale  half  size. 

Draw  also  full-size  sections  of  the  frame,  the  plane  of  sec- 
tion passing  through  the  hanger  at  the  lines  AB,  CD,  and  EF. 

•Fig-  I57  shows  Sellers  method  of  forming  the  ball-and- 
socket  joint  on  adjustable  hanger  bearings.  The  plungers 
P  and  P'  have  shallow  threads  which  extend  along  a  portion 
of  the  plungers,  while  the  threads  in  the  boss  are  cut  the  entire 
length  of  the  boss.  The  plungers  are  locked  in  position  by 
the  set-screws  S,  the  points  of  which  are  made  to  press  against 
the  plain  part  of  the  plungers  below  the  threads.  The 
plungers  are  cast  hollow,  and  are  used  as  lubricators  by  filling 
them  with  cotton  saturated  with  oil,  which,  under  ordinary 
conditions,  is  sufficient  to  lubricate  the  journal.  The  open- 
ings O  and  O'  are  filled  with  tallow  which  is  solid  at  ordinary 
temperatures  but  melts  should  the  bearing  become  heated. 
The  outer  end  of  the  plungers  has  a  hexagonal  hole  to 
receive  a  key  by  means  of  which  the  screw  is  turned  when 
adjusting  the  bearing. 

Exercise  73* — Design  a  hanger- frame  and  bearing,  altering 
the  frame  shown  in  Fig.  156  to  suit  the  arrangement  of 
plungers  and  bearing  shown  in  Fig.  157,  and  design  a  method 
of  fastening  a  drip-catcher  to  the  frame,  other  than  that  shown 
in  Figs.  155  and  156,  which  must  be  so  arranged  that  it  can 
be  easily  removed  and  replaced.  Show  a  complete  FRONT 
ELEVATION,  SECTIONAL  END  VIEW,  and  PLAN  projected  from 
the  front  elevation. 

Make  D  =  2 J",  and  length  of  bearing  =  4  D.  Unit  of 
proportions  is  \ .  4  D  -}-  .  2 .  Scale  half  size. 


222 


DKA  WING   AND   DESIGNING. 


PIG. 


BEARINGS,  SOLE-PLATES,  AND    WALL    BOX-FRAMES.  22$ 

Wall-  or  Post-hanger  is  employed  to  serve  the  same 
purpose  as  the  Wall  bracket  with  its  separate  pedestal. 
The  frames  of  these  hangers  are  designed  on  the  same 


FIG.  158. 

general  lines  and  principles  as  the  drop  hanger-frames  shown 
in  Fig.  156.  This  hanger  is  shown  in  Fig.  158,  with  and 
without  the  double  brace  links,  fitted  with  chain  lubricating- 
bearings  of  the  design  shown  in  Fig.  160. 

Exercise  74 — Draw  FRONT  ELEVATION  and  two  END 
VIEWS  as  shown  in  Fig.  159,  and  a  PLAN  VIEW  projected  from 
the  front  elevation.  Scale  8"  to  the  foot.  Show  also  full- 
sized  sections,  the  plane  of  section  passing  through  the  frame 
at  the  lines  AB,  CD,  and  EF. 


224 


DRA  WING   AND   DESIGNING. 


FIG.  160. 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  22$ 

Chain  Lubricating-bearing. — This  type  of  bearing  is  de- 
signed to  be  lubricated  by  means  of  endless  chains  C  which 
hang  over  the  shaft,  and  as  it  revolves  the  chains  revolve  with 
it,  passing  through   the   oil   in   the  reservoirs  OR  formed  at' 
each  end  of  the  box. 

The  chain  C  consists  of  a  series  of  parallel  links  which' 
form  surfaces  to  which  the  oil  adheres  by  capillary  attraction, 
and  is  carried  to  the  shaft,  spreading  through  the  channels 
C  C  to  all  parts  of  the  bearing.  All  surplus  oil  falls  back  into 
the  oil  reservoirs,  to  be  used  again  until  it  becomes  thick  or 
dirty,  and  is  then  drawn  off  by  removing  the  plugs  5. 

Exercise  75. — Draw  the  chain  lubricating-bearing  shown  in 
Fig.  161,  showing  a  HALF  ELEVATION  and  HALF  SECTIONAL 
ELEVATION;  an  END  VIEW  projected  from  the  light  HALF 
SECTIONAL  END  VIEWS  projected  from  the  left-hand  end, 
the  plane  of  section  passing  through  the  bearing  at  the  lines 
AB  and  CD,  and  a  PLAN  with  half  of  the  upper  box  re- 
moved. Scale  full  size.  Draw  also  an  ELEVATION  AND 
PLAN  of  a  part  of  the  lubricating  chain  as  shown  in  Fig.  163. 
Scale  four  times  full  size. 

Construction. — Fig.  162  shows  a  method  of  rinding  the 
centres  of  the  chain  represented  in  the  end-view  in  position 
on  the  shaft.  In  this  construction  the  centres  may  be  taken 
on  the  curve  unless  from  the  points  I  to  2,  where  the  radius 
is  small.  At  this  part  step  off  chords  equal  in  length  to  the 
pitch  of  the  chain,  and,  parallel  to  the  chords,  draw  lines 
tangent  to  the  arcs.  The  intersection  of  the  tangent  lines 
may  be  taken  as  the  centres  of  the  chain  at  that  part. 


226 


DRAWING   AND   DESIGNING. 
I 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.   22/ 

Bushes,  Steps,  or  Brasses  are  names  given  indiscrimi- 
nately to  the  bearings  proper,  i.e.,  the  brass  or  bronze  parts, 
that  are  in  contact  with  and  support  the  journal.  They  afford 
a  means  of  taking  up  the  lost  motion  due  to  wear,  thus  insur- 
ing that  the  journal  with  which  they  engage  will  have  the  re- 
quired motion  about  the  given  axis.  They  must  be  made  of 
a  material  that  will  allow  the  journal  to  run  in  contact  with  it 
with  a  minimum  amount  of  friction,  and  will  withstand  wear 
without  wearing  the  journal.  They  must  also  have  sufficient 
strength  to  resist  the  stresses  that  come  upon  them,  without 
undue  yielding.  When  supporting  a  wrought-iron  or  steel 
shaft,  gun-metal,  to  a  limited  extent,  fulfils  all  these  require- 
ments. Other  metals  possess  some  of  these  qualities  in  a 
higher  degree  without  having  them  all. 

White  metals,  such  as  "  babbitt's  "  or  "  magnolia"  metals, 
offer  less  frictional  resistance,  and  their  surfaces  may  be  de- 
stroyed without  injuring  the  surface  of  the  journal  (as  would 
be  the  case  with  the  bronzes),  but  they  are  too  soft  to  be 
used  alone  unless  subjected  to  an  exceptionally  light  load. 
The  position  of  the  bush  in  the  supporting  frame  depends 
upon  the  direction  of  the  pressure.  In  the  majority  of  bear- 
ings the  resultant  pressures  are  in  one  or  two  directions,  and 
all  lost  motion  can  be  taken  up  by  making  the  bearings  in  two 
parts.  The  ordinary  forms  of  two-part  bearings  are  shown 
n  Figs.  164  to  167.  The  forms  shown  in  Figs.  164  and  165 
are  turned,  and  the  supporting  frame  is  bored  with  a  cylin- 
drical hole  into  which  the  bearings  are  fitted.  To  prevent 
these  forms  from  rotating  with  the  shaft  they  are  provided 
with  rectangular  lugs  L,  as  in  Fig.  165,  or  with  steady  pins  P9 
as  in  Fig.  164. 


226 


DRAWING  AND   DESIGNING. 
I 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  22$ 

The  pins  may  be  either  cast  with  the  bush  or  driven  in. 
The  forms  shown  in  Figs.  166  and  167  are  cast  square  or 
octagonal  and  planed  to  fit  correspondingly  shaped  surfaces  in 
the  supporting  frames.  The  square  form  is  the  cheaper,  but 
should  it  become  hot  it  is  liable  to  be  distorted,  owing  to  the 
unequal  distribution  of  metal.  To  facilitate  fitting,  and  reduce 
machining  on  bearings,  it  is  usual  to  support  them  at  their 
ends  only,  by  forming  projecting  faces  F  S  at  each  end.  This 
may  be  done  successfully  on  small  bearings  subjected  to  a 
steady  load,  but  on  crank-shaft  bearings  it  is  advisable  to 
support  them  over  their  length.  The  bearings  should  be 
divided  on  a  line  normal  to  the  resultant  pressures  and,  as 
they  will  wear  very  little  at  that  part,  they  may  be  made 
thinner  than  at  the  part  where  the  pressure  is  greatest.  To 
keep  the  bearings  from  moving  laterally  a.long  the  shaft  they 
are  provided  with  flanges  F,  between  which  the  supporting 
frame  fits,  as  shown  in  Fig.  169. 

Sole-plates. — -When  a  pedestal  is  secured  to  masonry  or 
brickwork  it  is  necessary  to  spread  the  pressure  upon  the 
journal  over  a  large  surface.  For  this  purpose  a  Sole-  or 
Base-plate  is  employed.  These  usually  consist  of  a  flat  cast- 
iron  plate  with  a  bevelled  surface  upon  which  the  pedestal  can 
be  adjusted  horizontally  by  means  of  the  wood  keys  K,  which 
are  driven  in  between  the  joggles  J  and  the  ends  of  the 
pedestal  base,  as  shown  in  Fig.  169.  The  pedestal  is  fast- 
ened to  the  sole-plate  by  the  bolts  P  B,  which  pass  through 
it  and  the  base  of  the  pedestal.  The  sole-plate  is  secured  to 
the  foundation  by  the  bolts  F  B.  The  width  (b)  of  the  sole- 
plate  should  be  equal  to  (a)  width  of  pedestal  base  -)-  the 
amount  of  movement  of  pedestal  along  shaft  -f-  say  J". 


230  DRAWING   AND   DESIGNING. 

Adjustable  Base-plates  are  used  for  adjusting  bearings 
vertically  and  horizontally.  The  vertical  adjustment  is  made 
by  sliding  wedges  which  may  be  arranged  either  laterally  (as 
in  Fig.  168)  or  longitudinally.  The  horizontal  adjustment  is 


FIG.  168. 

effected  by  means  of  set-screws  which  take  the  place  of  the 
wooden  keys  shown  in  Fig    169. 

Pedestal  or  Pillow-block  Bearings  are  used  where  it  is 
necessary  to  have  a  bearing  that  is  rigid  and  yet  adjustable. 
Fig.  169  shows  the  ordinary  form  of  pedestal  bearing  em- 
ployed for  supporting  shafting  from  3"  to  8"  in  diameter. 
The  inner  surfaces  of  the  block  P  and  cap  C  are  formed  to 
suit  the  outer  surface  of  the  bushes.  When  the  block  is  pre- 
pared by  hand-work  to  receive  the  bushes  it  is  provided  with 
fitting  strips  F  S  to  facilitate  fitting,  but  when  prepared  by 
planing,  the  strips  are  unnecessary.  Some  engineers  make 
the  bushes  that  they  do  not  touch  each  other  when  the  shaft 
is  in  position,  and  as  the  bushes  wear,  a  space  being  left  be- 
tween the  cap  and  the  pedestal,  they  are  brought  nearer  to- 
gether by  screwing  down  the  cap  C  by  means  of  the  bolts 
C B.  To  keep  the  cap  from  being  screwed  down  too  far, 
causing  the  bushes  to  bind  the  journal,  the  space  between  the 
cap  and  the  pedestal  is  sometimes  filled  with  hard  \yood  and 
the  wear  is  taken  up  by  filing  down  the  hard-wood  distance- 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  2$l 

pieces,  thus  allowing  the  cap  to  be  screwed  down  a  limited 
distance.  Others  make  the  bushes  in  contact  with  each  other, 
as  in  Fig.  169,  when  the  bushes  fit  the  shaft,  and  when  they 
become  worn  they  are  filed  down  sufficiently  to  compensate 
for  the  wear.  When  the  bushes  do  not  come  in  contact  with 
each  other  and  no  distance-piece  is  used,  the  cap-bolts  should 
be  provided  with  double  nuts.  After  the  pedestal  has  been 


IHD1AM* 


FIG.  169. 

adjusted  to  suit  the  shaft,  it  is  held  in  position  by  the  bolts 
P B.  The  holes  in  the  base-  and  sole-plate  through  which 
the  bolts  PR  pass  are  made  oblong  to  allow  the  pedestal  to 
be  moved  along  the  shaft  or  transversely  to  it. 

To  facilitate  the  fitting  of  the  pedestal  to  the  piece  upon 
which  it  is  carried,  the  base  is  provided  with  fitting-strips 
around  the  edges  and  across  the  centre.  The  oil-cup  is  usually 


232  DRA  WING   AND   DESIGNING. 

cast  with  the  cap  C,  or  screwed  into  the  tapped  hole  O,  Fig. 
169.  On  pedestals  having  journals  less  than  3"  in  diameter 
O  may  be  made  to  receive  an  oil-cup  with  a  J"  pipe  tap- 
shank,  and  when  over  3'^  with  a  -|"  pipe  tap-shank. 

Exercise  76. — Draw  a  general  arrangement  of  a  pedestal 
and  sole-plate,  Fig.  169,  substituting  the  form  of  bearing 
shown  in  Fig.  164.  Show  a  HALF  ELEVATION  and  HALF 
SECTIONAL  ELEVATION,  the  plane  of  section  passing  through 
the  centre  of  the  block ;  also  a  HALF  PLAN  and  HALF  SEC- 
TIONAL PLAN,  the  plane  of  section  passing  transversely  through 
the  centre  of  the  journal.  From  the  elevation  project  a  HALF 
END-ELEVATION  and  HALF  SECTIONAL  END-ELEVATION,  the 
plane  of  section  passing  through  the  centre  of  the  pedestal. 
Make  the  length  of  the  holes  through  the  sole-plate  and  pedes- 
tal-base sufficient  to  allow  the  pedestal  to  move  \>f  in  either 
direction.  Make  D  =  4"  and  L  =  2D.  Scale  half  size. 

Construction. — All  parts  dimensioned  in  decimals  are  in 
terms  of  D  (the  diameter  of  the  journal).  Parts  marked  in 
inches  are  constant.  Any  parts  not  dimensioned  can  be  de- 
termined by  the  student  from  knowledge  derived  from  previ- 
ous exercises.  A  method  of  drawijyff*tthe  joggles  J  is  shown 
at  Fig.  169,  which  will  be  readily  understood  from  the 
drawing. 

SELF-LUBRICATING    PEDESTAL. 

In  this  design,  Fig.  170,  an  oil  reservoir  OR  is  formed  on 
the  under  side  of  the  bearing,  in  which  loose  rings  R  are 
revolved  by  their  friction  on  the  journal,  thereby  raising  a 
continuous  supply  of  oil  to  the  upper  side  of  the  bearing, 
thus  keeping  the  journal  thoroughly  lubricated  and  not 


,  SOLZ-fLATES,  AND     WALL    BOX-FRAMhS.  233 


234  DRAWING   AND   DESIGNING. 

wasteful,  as  the  surplus  oil  that  flows  out  of  the  bearing  is 
caught  in  the  chambers  CC  and  carried  back  to  the  reservoir 
OR. 

As  the  same  oil,  in  this  form  of  lubricator,  is  being  used 
repeatedly,  after  a  time  it  becomes  dirty  and  thick  and  is  then 
useless.  By  removing  the  screws  5  the  old  oil  is  drained  off, 
and  the  reservoir  can  then  be  replenished  by  pouring  new  oil 
into  the  openings  in  the  cover.  These  openings  are  made 
large,  so  that  the  engineer  can  see  if  the  rings  are  revolving. 

This  pedestal  is  designed  for  down  pressure,  and  as  there 
will  be  very  little  wear  on  the  upper  bush  it  is  cast  with  the 
cap  C.  The  lower  bush  B  is  a  separate  piece,  as  shown  by 
the  sketch,  Fig.  171.  To  reduce  the  machining  it  is  pro- 
vided with  projecting  faces  MS,  called  machining  strips, 
which  fit  upon  corresponding  projections  on  the  pedestal, 
and  are  made  concentric  with  the  shaft,  so  that  to  remove  the 
bush  it  is  not  necessary  to  withdraw  the  shaft,  as  the  bush 
when  relieved  from  the  load  can  be  turned  to  the  upper  side 
of  the  journal. 

By  this  arrangement  the  pedestal  is  practically  independ- 
ent of  wear,  as  the  bushes  can  be  removed  and  re-babbitted 
with  little  trouble  or  expense, 

To  keep  the  bush  from  moving  laterally,  flanges  F  are 
cast  at  each  end  which  fit  inside  of  the  end  machining  strips 
on  the  pedestal. 

The  lower  bush  is  kept  from  turning  by  the  distance 
piece  DP,  which  also  keeps  the  cap  from  being  screwed 
down  too  far  and  clamping  the  shaft.  To  take  up  the  wear 
of  the  bushes,  the  distance  pieces  DP  are  planed  to  let  the 
cap  go  further  into  the  pedestal.  To  allow  this,  a  space 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES.  2 35 

A  is  left  between  the  pedestal  and  the  cover.  This  space 
need  not  be  greater  than  the  thickness  of  the  babbitt  lining, 
which  should  be  from  f"  to  i"  thick. 

The  cap  is  made  to  fit  into  the  pedestal  so  as  to  sit' 
squarely  upon  the  journal,  and  does  not  depend  upon  the 
cap  bolts  to  prevent  lateral  movement. 

The  cap  is  usually  held  down  by  two  bolts,  but  to  avoid 
large  bolts  in  the  larger  sizes  of  pedestals  it  is  quite  common 
practice  to  use  four.  The  bolts  in  this  case  are  made  square 
in  section,  and  have  T  heads  which  fit  into  recesses  cast  in 
the  pedestal.  The  pedestal  is  held  in  the  proper  position  by 
the  bolts  PBt  which  pass  through  oblong  holes  in  the  pedestal 
to  allow  for  longitudinal  adjustment  in  either  direction. 
This  form  of  pedestal  is  suitable  for  journals  from  5"  in 
diameter  up. 

Length  of  Bearings. — The  frictional  resistance  at  the 
surface  of  the  journal  converts  the  mechanical  energy  into 
heat,  and,  unless  the  area  of  the  journal  is  sufficiently  large 
to  allow  the  heat  to  radiate  as  fast  as  it  is  generated,  the 
temperature  will  become  great  enough  to  destroy  the  lubri- 
cant, allowing  the  rubbing  surfaces  to  come  in  contact  and 
adhere  to  each  other.  The  radiating  surface  would  be  en- 
larged by  increasing  the  diameter  of  the  journal,  but  the 
velocity  of  the  rubbing  surfaces  would  also  be  increased; 
therefore  the  frictional  resistance  and  the  space  through 
which  it  acts  would  be  greater.  Thus  it  will  be  seen  that 
:o  add  to  the  radiating  surface  without  increasing  the  work 
f-t  the  surface  of  the  journal  we  must  increase  the  length  of 
the  bearing. 

In  a  paper  read  before  the  Manchester  (England)  Associa- 


236  DRAWING   AND    DESIGNING. 

tion  of  Engineers,  Professor  Goodman  stated  that  the  area 
of  a  bearing  should  be  such  that  not  more  than  one  thermal 
unit  of  heat  is  generated  per  square  inch  of  bearing  surface 
per  minute. 

Let   P  —  total  pressure  in  pounds; 

>w  =  coefficient  of  friction; 

6"  =  speed   of   circumference  of  journal   in    feet   per 

nDN 

minute  =  -      -  ; 
12 

N  =  number  of  revolutions  per  minute; 

A  =  area  of  bearing  in  square  inches,  i.e.,  the  diam- 

eter W-  X  the  length  L  ; 
D  =  diameter  of  journal  in  inches; 
L  =  length  of  journal  in  inches; 
W  •=•  width  of  the  chord  in  contact,  in  inches. 
Foot-pounds  of  work  done  per  minute  at   the  circumfer- 
ence   of    the   journal  =  P^S.      The  thermal  units  per  minute 


PvS 
:>  and  A  =  :—  g-p-,.from  which  L  =  z>  m  inches. 


With  steel  journals  running  in  bronze  or  white-metal 
bearings,  having  continuous  lubrication,  //,  the  coefficient  of 
friction  may  be  taken  at  .0056. 

Exercise  77  —  Design  a  self-lubricating  pedestal  for  a  shaft 
6"  in  diameter,  of  the  form  shown  in  Fig.  170,  to  carry  a 
load  of  35,000  pounds,  and  run  at  a  speed  of  300  revolutions 
per  minute. 

Show  a  HALF  ELEVATION,  HALF-SECTIONAL  ELEVATION, 
the  plane  of  section  passing  through  the  centre  of  one  of  the 
lubricators,  a  HALF  END  ELEVATION  and  HALF  TRANSVKRSF, 
SECTION,  the  plane  of  section  passing  through  the  pedestal 
at  the  centre,  a  HALF  PLAN  of  the  left-hand  side  of  the  pedes- 
ta-1,  a  QUARTER  PLAN  with  the  cover  (C)  removed,  a  QUAR- 


BEARINGS,  SOLE-PLATES,  AND    WALL   BOX-FRAMES. 

TER-SECTIONAL  PLAN,  the  plane  of  section  passing  through 
the  centre  of  the  shaft.      Scale  3"  to  the  foot. 

Make  also  full-size  drawings  of  the  lower  bush,  showing  a 
HALF  ELEVATION  and  HALF-SECTIONAL  ELEVATION,  a  HALF 

END  VIEW,  and  a  HALF  TRANSVERSE  SECTION,  and  a  plan 
and  elevation  of  the  ring-joint  as  shown. 

All  points  are  proportional  to  the  diameter  (D)  of  the 
journal,  except  those  parts  which  are  constant  for  journals 
of  various  sizes. 


CHAPTER  VII. 
BELT   GEARING. 

Belts. — Among  the  many  different  kinds  of  material  used 
for  belting  are  leather,  cotton,  gutta-percha,  India-rubber, 
canvas,  camel-hair,  catgut,  flat  wire  or  hemp  rope,  steel 
bands,  flat  chains,  etc. 

The  most  common  in  general  practice  are  leather  and 
cotton,  the  latter  often  found  coated  with  India-rubber  and 
known  as  gum  belts. 

Leather  is  more  durable  than  gum  under  most  conditions, 
but  for  main  driving  the  latter  is  superior,  having  an  adhesion 
which  is  claimed  to  be  one  third  greater  than  the  former. 

Transmission  of  Motion  by  Belts. — Motion  may  be 
transmitted  from  one  pulley  to  another  with  uniform  linear 
velocity  by  means  of  a  belt,  provided  there  is  no  slipping  of 
the  belt  on  the  pulley;  i.e.,  regarding  the  belt  as  inextensible 
every  part  of  it  will  have  the  same  velocity  as  the  outside 
rim  of  the  pulley. 

Referring  to  Fig.  171,  let  d^  and  d^  be  the  diameter  of  the 
driver  and  driven  pulleys  respectively,  and  let  TV,  and  A7,  be 
their  revolutions  per  minute  and  V  the  velocity  of  the  belt. 

The  speed  of  the  rim  of  the  driver 

=  4  n  N,  =   V  .     ...     .      .     (i) 

238 


BELT   GEARING. 


B 


FIG.  171. 
and  the  speed  of  the  rim  of  the  driven 


therefore 


239 


(2) 


4  n  N,  =  d,  n  N,     or     d,N,  =  d,N,     or  =      .    (3) 

•"i         a, 

In   all   questions  concerning  the  velocity  ratio  of  belting 
the  pulley  diameters  should  be  taken  to  the  centre  of  the  belt 


240  DRAWING   AND    DESIGNING. 

thickness;  thus  the  virtual  diameter  of  the  pulley  would  be 
the  nominal  diameter  plus  one  thickness  of  the  belt.  For 
other  calculations  the  thickness  of  the  belt  is  so  small  it 
may  be  neglected  without  much  error. 

Example  i.  —  In  the  draughting-room  at  Sibley  College 
there  is  a  valve-molion  model  driven  by  an  electric  motor. 
The  shaft  A  of  the  motor  carries  a  pulley  i-J"  diameter  from 
which  passes  a  belt  to  a  15"  pulley  on  a  counter-shaft  B. 
This  shaft  carries  another  pulley  6"  in  diameter  connected  by 
a  belt  to  the  driving-wheel  pulley  of  30"  diameter  on  the 
valve-motion  model  axle. 

The  speed  of  the  motor  is  1450  R.  P.  M.  Find  the  speed 
of  the  valve-motion  model  in  R.  P.  M.,  Fig.  171. 

From  formula  (3)  we  get 

^•_4X4_ILX30_  ,0 
A".-4X4-i.SXT- 

Substituting  we  get 


Some  Practical  Rules.  —  The  width  of  belts  should  be 
about  25  per  cent  less  than  the  face  of  the  pulley. 

It  has  been  demonstrated  by  experience  that  large  pulleys 
and  fast  running  belts  are  much  more  economical  than  small 
pulleys  and  slow-speed  belts.  All  pulleys  should  be  carefully 
centred  and  balanced  on  the  shaft.  Driving-pulleys  carrying 
shifting-belts  should  have  a  perfectly  flat  surface.  All  other 
pulleys  should  have  a  convexity  of  \"  to  12"  of  width; 
when  curved  the  chord  of  the  arc  should  be  the  same.  For 


BELT  GEARING.  241 

pulleys  smaller  than  12"  wide,  fromf"  to  J"  per  foot  of  width 
should  be  used. 

Pulley  diameters  should  be  as  large  as  can  be  used  pro- 
vided the  belt  speed  is  kept  within  5000  feet  per  minute, 
which  is  held  to  be  the  limit  of  speed  for  belt  economy. 

With  regard  to  the  position  of  idle  pulleys  in  relation  to 
the  driving-pulley  Taylor  says,  "  Idle  pulleys  work  most 
satisfactorily  when  located  on  the  slack  side  of  the  belt  about 
one  quarter  away  from  the  driving-pulley." 

Transmission  of  Power  by  Belts. — Let  two  pulleys  A 
and  B  be  connected  by  a  belt  with  a  tension  equal  to  7,. 
Until  force  is  applied  at  A  tending  to  produce  rotation  of  the 
pulleys,  the  tension  7,  and  7,  will  be  equal ;  but  as  the  force 
at  A  increases  the  tension  in  7,  will  increase,  and  that  in  7, 
will  decrease  until  Tl  —  7",  =  P  =  resistance  to  rotation  at 
the  rim  of  the  pulley;  i.e.,  when  the  belt  is  at  the  point  of 
slipping,  the  ratio  of  Tl  to  7,  will  be  a  maximum  and 
—  efa,  or  7,  -r-  7a  =  efa.  Where  e  is  the  base  of  the  Naperian 
system  of  logarithms,  /is  the  coefficient  of  friction  =  .3,  a  is 
in  n  measure  and  =  a  in  degrees  X  0.0174. 

By  logarithms  we  find  that  7,  -f-  7,  =  efa  =  log. 
7,  -r-  7,  =  fa  log.  e  =  .4343/tf- 

Example  2. — A  six  H.P.  dynamo  is  to  have  a  speed  of 
1450  R.  P.  M  and  has  a  6"  pulley  on  its  shaft.  Power  is  ob- 
tained from  an  engine  fly-wheel  running  at  58  revolutions  per 
minute.  To  obtain  the  required  velocity  ratio  between  the 
engine  and  dynamo,  the  diameter  of  the  fly-wheel  will  have 
to  be  25  times  that  of  the  dynamo  pulley  with  direct  connec- 
tion ;  but  such  a  diameter  would  be  practically  impossible,  so 
it  will  be  necessary  to  install  a  counter-shaft.  Let  18"  be  the 


242 


DRAWING   AND   DESIGNING. 


most  suitable  diameter  for  the  largest  pulley  on  the  counter- 
shaft, then  the  necessary  speed  of  the  counter-shaft  will  be 

=    1450  X  —  =  483   R.  P.  M.       Between   the    engine    and 
18 

.  n  - 

counter-shaft  the  pulley  diameter  ratio  =  -    ~  =  8.32.      Let 

:  v   5° 

the  diameter  of  the  fly-wheel  be   50"  then   its   connecting- 
pulley  on  the  counter-shaft  will  be  ~ — .  =  6"  nearly. 

<Y  _.,.;..    ......  ;..   :..-v    0.32       .„  _    (     •(•••••-••;•• 

To  determine  the  size  of  belt  necessary  to  connect  the 
dynamo  with  the  counter-shaft  we  will  have  to  find  the  value 
of  Tl  =  to  the  working  pull  on  the  lower  side  of  the  belt. 


FIG.  172. 


First   find   the  work   done  by  the  dynamo  —  6  X  33,000  =• 
198,000  foot-lbs.  per  minute;    the  rim  of  the  dynamo  pulley 

6rr 
runs  at  —   X    1450   ==    2277    feet    per    minute;      therefore 


T  —  T  — 

*      «  ^      n          ~— 


98OOO 

2277 


=  87  Ibs.      Let  the  centres  of  the  dynamo 


shaft  and  counter-shaft  be   15  feet  apart,  then  (see  Fig.   172) 


BELT  GEARING. 


243 


y^ r      g// <," 

tan.  6  =  — - —  =  <—   —?—  =  .04,  and  from  a  table  of  natural 

/  I  oO 

trig,  functions  we  find  that  tan.  .04  =  2.25°. 
a  =    180°  —   20  =    175.75,     a  in  TT  measure  =    175.75    X 
0.0174  =  3-05.     Then  log.  Tt  -5-  T,  =  .4343  X  .3  X  3.05  = 
•3974?  from  a  table  of  logarithms  we  find  that  .3974  is  the 
log.  of  the  number  2.50,  therefore 


Combining  these  equations  thus: 

2.50  T,  -  2.50  T;  =  87  x  2.5",    7;  -  2.50  r,  =  o, 

1.50  r,  =  217.5,  we   find    217.5  -*-  J-S0  =   J45»    and 
allowing  70  Ibs.  per  inch  width  of  belt,  then 
145  ~-  70  —  2.06,  say  2j". 

Some  Practical  Rules  for  the  Transmission  of  Power.— 

Richards  gives  the  following  rule  for  the  size  of  driving-belts, 
which  he  says  is  near  enough  for  all  cases  that  arise  in  ordi- 
nary practice. 

FX   W 

A 


H.P.  = 


(4) 


Where  V  =  the  velocity  of  the  belt  in  feet  per  minute. 
W  =  the  width  of  the  belt  in  feet. 
A  =  the  area  given  to  suit  different  conditions  in 
the  following  table : 


TABLE  30. 


LEATHER   BELTS    SINGLE   THICKNESS. 

i  H.  P. 

On  smooth  iron  pulleys 80  ft. 

On  wooden  pulleys 65  ft. 

On  covered  pulleys 50  ft. 


GUM    BELTS    AVERAGE    THICKNESS. 

i  H.P. 

On  smooth  iron  pulleys 60  ft. 

On  wooden  pulleys 50  ft. 

On  covered  pulleys 35  ft. 


244 


DRAWING   AND   DESIGNING. 


Belts  should  be  made  as  wide  as  possible  ;  they  are  often 
too  narrow,  but  never  too  wide. 

Thickness  of  Belts.  —  As  belts  increase  in  width  their 
thickness  should  also  increase.  Double  belts  should  be  used 
on  pulleys  over  12"  diameter.  Large  belts  running  at  very 
high  speeds,  as  in  electrical  work,  should  have  slots  punched 
through  them  in  such  manner  and  position  as  to  prevent  air 
cushion. 

The  following  proportions  for  thickness  of  belt  and  cor- 
responding working  tension,  based  on  a  safe  working  stress 
of  320  Ibs.  per  sq.  in.  for  laced  joints,  are  given  by  Unwin  : 

TABLE  31. 


Thickness  of  belt  

iV 

A 

i 

A 

r 

V* 

i 

iV 

F 

H" 

|" 

Working  tension  in  Ibs. 

per  inch  of  width  .... 

60 

70 

80 

100 

1  20 

140 

160 

i  so 

200 

220 

240 

For  other  rules  and  formulae  see  Kent's  Engineers'  Pocket 
Book,  page  876. 

For  a  safe  working  tension  under  ordinary  conditions, 
many  authorities  allow  only  45  Ibs.  per  inch  of  width;  but 
according  to  Mr.  A.  W.  Smith,  experiments  have  shown  that 
a  safe  tension  of  7°  Ibs.  may  be  had  per  inch  of  width  of 
belt. 

Proportions  of  Pulleys  (Figs.  173  and  174). — 
a    =  centre  of  set-screw  from  end  of  hub  =  ij</,. 
<7,  =  centre  of  bolt  from  edge  of  flange  =  ijdfa. 
b    =  width  of  belt — see  Example  2. 

B  =  pulley  face  =  f  (b  +  0.4).      (Unwin)      .'.      „     .     (5) 
d  =  shaft  diameter. 


BELT  GEARING. 


245 


246 


DKAW1NG   AND   DESIGNING. 


BELT  GEARING.  24? 

d,  =  diameter  of  set-screw  in  solid  pulley  =  \d  +  -iV".    •   (6) 

</,  =  diam.  of  bolt  in  split  pulley  at  rim  and  hub  =  eq.      (6) 

d^  —  set- screw  for  key  =  .2$d. 

D  =  diameter  of  pulley. 

E  =  centre  of  rim  bolt  from  inside  of  rim  =  d^ -+  /,  -f-  i"»     (7) 

IS 

f    =  radius  at  end  of  arms  =  — 

2 

F  =  4  +  t". 

g    =  width  of  arm  at  rim  =  \h. 

h   =  width  of  arm  at  centre  of  pulley 


»  /BD  •) 

•6337  v  ~T~  single  belt* 

-    <*•*>  ,/  .-V,   ...    (8) 


/£    =  thickness  of  arm  =  -  . 

/    =  length  of  hub  =  \B  to  B. 

n   =  number  of  arms  =  —^  +  4.    The  nearest  number  divisible 

by  2  should  be  taken. 

p   =  thickness  of  rib  surrounding  hub  between  arms  =  .31  d. 
t     =  thickness  of  belt  —  see  Table  31. 
/,   =  thickness  of  rim  =  .6t  -f-  .005  D.     .      .      .     .      .     (9) 

/,   =  inside  taper  of  pulley  rim  =  /,  -±-  2. 

.14  V~BD  +  i  for  single  belt.    (10) 
w  ==  thickness  of  hub  =  J 

i  4<  double    "       (n) 


7?  =  radius  of  pulley  crown  =  from  3  to  5  & 

Exercise  84.  —  A  fan  revolving  with  a  speed  of  1800  rev. 
per  min.  develops  8  H.P.  and  has  an  8"  pulley  on  its  shaft. 
Power  is  obtained  from  an  engine  fly-wheel  running  at  75 
rev.  per  min.  Diam.  of  fly-wheel  =  5  feet.  Determine  the 
proper  diameters  of  the  intermediate  pulleys  and  make  a  suit- 


248  DRAWING   AND   DESIGNING. 

able  working  drawing  of  the  largest  of  them,  similar  to  Fig. 
173  or  Fig.  174.  Scale  6"  —  I  foot. 

See  Example  2,  p.  241. 

Wood-split  Pulley  (Fig.  175). — The  Committee  on 
Science  and  the  Arts  of  the  Franklin  Institute,  in  report 
ing  on  the  Dodge  Wood-split  Pulley  with  wooden  bushings, 
stated  that  in  most  cases  wood-split  pulleys  are  better  than  iron 
pulleys.  Some  of  the  reasons  given  for  this  are  as  follows : 

(1)  They  are  lighter  than  iron  pulleys,  lessening  the  weight 
on  the  line  shaft  an4  bearings  and  reducing  friction. 

(2)  The  compression  fastening  of  the  wooden  pulley  on 
iron  or  steel  shafts  with  wooden  bushings  will  hold  the  pulley 
on  the  shaft  quite  firmly,  dispensing  with  the  use  of  keys. 

(3)  The  grip  of  a  belt  on  a  wooden  pulley  exceeds  that  on 
an  iron  pulley  to  an  amount  equal  to  at  least  33  per  cent. 

(4)  The  method  of  fastening  the  wooden   pulley  to   the 
shaft  neither  mars  nor  weakens  the  shaft,  and  prevents  any 
tendency  to  throw  the  pulley  out  of  balance,  as  is  the  case 
when  keys  and  set-screws  are  used. 

Construction. — "They  are  built  of  wooden  segments,  the 
face  being  made  of  poplar.  The  two  halves  of  the  pulley 
are  secured  to  the  shaft  with  bolts  The  bushings  to  fit 
different-sized  shafts  are  made  of  hard  wood,  thoroughly 
air-dried,  then  bored  and  kiln-dried ;  then  each  bush  is 
counterbored  to  exact  size  of  shaft,  then  carefully  turned  on 
the  outside  to  fit  the  bore  of  the  pulley.  They  are  then  cut 
transversely  in  halves." 

Exercise  85. — Make  complete  working  drawings  of  a  wooden 
split  loose  pulley  14"  diam.,  shaft  2"  diam.  Projections  to 
be  the  same  as  shown  in  Fig.  175.  Scale  9"  =  i  foot. 


BELT  GEARING. 


249 


250 


DRAWING   AND    DESIGNING. 


All-wrought-steel  Pulley. — This  pulley  as  manu- 
factured by  the  Am.  Pulley  Co.  is  shown  in  Fig.  176.  In  a 
paper  on  the  subject  by  Mr.  E.  G.  Budd  before  the  Franklin 
Institute  in  June  1897,  the  following  advantages  are  claimed 
for  the  all-wrought-steel  pulley: 

(1)  They  can  be  used  in  the  heaviest  service,  clamped  to 
the  shaft  without  keys  or  set-screws,  and  never  show  a  sign 
of  slipping. 

(2)  There  is  no  machining  required.     The  rims  and  arms 


FIG.  176. 

are  cut  with   shears  and  pressed  into   shape  with   hydraulic 
pressure. 


BELT  GEARING.  2$  I 

(3)  Economy  of  material  and  symmetry  of  form,  requiring 
no  counterbalance. 

(4)  Being    made  of    the    best    and    strongest    material, 
it  is    fully  as    light    as    the  wood    pulley,    and    much    more 
durable. 

Construction. — Referring  to  Fig.  176  it  may  be  seen  that 
the  rim  is  made  up  of  four  segments.  It  is  divided  once 
transversely  and  once  longitudinally.  The  flanges  on  the 
rim  at  the  centre  of  the  face  give  a  means  of  fastening  it  to 
the  arms.  The  rim  edges  are  rolled,  giving  a  neat  appearance 
and  preventing  the  scraping  of  the  belt  in  throwing  it  off  or 
on. 

The  hub  is  made  of  half  cylinders  of  heavy  steel,  and  is 
connected  to  the  rim  by  a  spider  divided  into  four  parts,  two 
parts  to  each  half  of  the  pulley.  The  spider 'arms  are  flat 
and  have  the  edges  lying  in  the  direction  of  rotation.  The 
manner  of  fastening  the  arms  to  the  hub  and  rim,  and  their 
corrugated  section,  as  shown  at  A  in  Fig.  177,  make  them  ex- 
ceptionally strong  for  their  purpose. 

Exercise  86. — Make  a  true  working  drawing  of  the  all- 
wrought-steel  pulley  shown  in  Fig.  177  "to  T:he :  "dimensions 
given.  Scale  4!'  =  i  foot. 

Cone-pulleys — In  operating  machine  tools  it  is  often 
necessary  to  change  power  and  speed.  This  is  accomplished 
most  easily  by  means  of  cone-pulleys.  The  driven  pulley 
has  a  series  of  steps  whose  diameters  are  proportioned  so  that 
the  belt  shall  fit  all  pairs  of  steps  with  an  equal  tension,  and 
when  the  belt  is  shifted  from  one  pair  of  steps  to  another 
the  velocity  ratio  will  be  changed. 


252 


DRAWING  AND   DESIGNING. 


BELT  GEARING. 

Length  of  Belts  (Fig.  178).— 
Let  L  —  length  of  belt ; 

D  =  diam.  of  large  pulley; 

d  =  diam.  of  small  pulley ; 

/=  distance  between  centres  of  pulleys: 

D  -\-  d 
ti  =  angle  whose  sine  = -j—  few  crossed  belts  and 


D-d 

2l 


for  open  belts. 


FIG.  178. 

From  a  table  of  sines  find  the   angle  9  in  degrees  and 
cos  6. 

Then  for  a  crossed  belt  : 


(12) 


and  for  an  open  belt 


L  =  -(£>  +  d)  +  0(D  -  d)  +  2l  cos  V 


.     (13, 


254  DRAWING   AND   DESIGNING. 

The  length  of  the  crossed  belt  is  constant  when  D  +  d  and 
/  are  constant ;  therefore  in  designing  a  pair  of  cone-pulleys  so 
that  the  crossed  belt  will  have  equal  tension  on  all  pairs,  it  is 
only  necessary  to  use  a  pair  of  equal  and  similar  cones  taper- 
ing opposite  ways. 

To  design  a  pair  of  cone-pulleys  for  an  open  belt: 
Let  AAAA  and  d^d^d^d^  =  diameters  of  opposite  pul- 
leys (Fig.  1/9).  And  using  the  graphical  method  given  by 
Mr.  C.  A.  Smith  in  the  A.  S.  M.  E.,  vol.  10,  p.  296,  let  us 
suppose  the  following  data  to  be  known : 

(1)  Diameters  of  AAAA  and  d,. 

(2)  /  =  distance  between  centres. 

Then  let  it  be  required  to  find  the  diameters  of  d^d3  and  d^ 

C  and  c  are  the  centres  of  the  opposite  cones. 

Around  centre  C  draw  circles  D^D^D^D^  and  at  centre  c 
draw  d^  to  the  diameters  given. 

Draw  tangent  Dldl. 

Bisect  Cc  in  the  point  E  and  erect  a  perpendicular  EF. 

Make  the  distance  EF  =  -3I4/  found  by  experiment. 
With  centre  F  draw  arc  A  tangent  to  D&.  All  lines  drawn 
tangent  to  arc  A  will  be  a  common  tangent  to  a  pair  of  cone 
steps  giving  the  same  belt-length  as  that  of  the  given  pair. 
So  to  find  the  diameters  of  the  steps  dtdt  and  dt  it  is  only 
necessary  to  draw  tangents  to  A  and  arc  A,  D,  and  arc  A, 
Dt  and  arc  A,  and  with  centre  c  and  radii  =  cdt ,  cd^  and  cdt 
respectively,  draw  the  circles  of  the  required  steps.  This 
method  is  an  approximation,  but  close  enough  for  all  practical 
purposes. 

Exercise  87. — Referring  to  Fig.  179:   First,  assume  diam- 
eters Dl  =  18",  A  =  14",  A  =  10"  and  A  and  dl  =  6",  and 


BELT  GEARING. 


255 


find  the  corresponding  diameters  of  the  opposite  steps  accord- 
ing to  Smith's  graphical  method  just  explained  in  connection 
with  Fig.  179. 

Second,  make  complete  working  drawings  of  one  of  the 
cone-pulleys,  showing  half  longitudinal  cross-section  and  half 
side  elevation  combined,  and  also  a  half  end  elevation  like 
Fig.  1 80.  Scale  6"  =  I  foot. 


PROPORTIONS   OF   CONE   PULLEY. 

Let    /  =  thickness  of  edge  of  rim  =  a\ 

h  =  thickness  of  hub  =  .  14  V RD,  +  J"  from  eq.  (10) ; 
H  —  length  of  hub  =  1 .43^ ; 
R  =  face  radius  =  $B. 

The  remaining  dimensions  may  be  taken  from  the  follow- 
ing table. 

TABLE  32. 

(Dimensions  in  inches.) 


b 

2 

2* 

3 

4 

5 

6 

8 

10 

12 

16 

18 

a 

A 

A 

I 

TV 

TV 

TV 

i 

i 

A 

TV 

e 

i 

i 

T\" 

A 

t 

f 

i 

4 

i 

f 
g 

1 
i 

t 

1 

i 
i 

i} 

I 

M  M 

oc^acic. 

U 
li 

II 

2£ 
i| 

9 

2f 
l| 

Rope  Pulleys. — Rope  pulleys  are  made  of  cast  iron  with 
grooved  rims,  as  shown  in  Figs.  181  and  182.  The  angle  of 
the  groove  is  usually  45°.  The  grooves  for  guide  pulleys  are 
semicircular  at  the  bottom,  the  radius  of  the  curve  being  a 
little  greater  than  the  radius  of  the  rope.  The* diameter  of  a 


256 


DRAWING  AND   DESIGNING. 


BELT  GEARING. 


257 


FOLLOWER 


FIG.  180. 


258 


DRAWING  AND   DESIGNING. 


rope  pulley  measured  to  the  centre  of  the  rope  should  not  be 
less  than  that  given  by  the  following  rule : 

Dl  =  (loD  +  1 6)  A     where 

Dl  =  the  smallest  diameter  of  the  pulley ; 

D  =  the  diameter  of  the  rope. 

As  in  the  case  of  belt  gearing,  the  slack  side  of  the  rope 
should  be  on  top  wherever  possible,  so  as  to  increase  the  arc 
of  contact  between  the  rope  and  the  pulley. 

Fig.  1 8 1.  This  is  the  form  of  groove  long  used  in  Great 
Britain.  It  has  flat  sides  inclined  to  each  other  at  from  45° 
to  60°. 

The  general  practice  in  America  is  to  use  the  form  of 
groove  shown  in  Fig.  182,  where  the  sides  are  curved.  This 
form  allows  the  rope  to  rotate  in  the  groove,  distributing  the 
wear  over  the  entire  surface  of  the  rope,  making  it  last  longer 
than  it  does  in  the  flat-sided  groove. 

Exercise  88. — Make  a  drawing  of  the  section  of  the  rim  of 
a  rope  pulley  with  five  grooves,  as  shown  in  Fig.  181.  Diam. 
of  rope  to  be  if".  Scale  full  size. 

Take  the  other  dimensions  from  the  following  table. 

TABLE  33. 

(Dimensions  in  inches.) 


D 

A 

B 

C 

E 

F 

G 

H 

I 

7/16 

5/i6 

\\ 

I 

I3/l6 

3/4 

9/16 

Ji 

1/2 

11/32 

1^ 

1 

»i 

31/32 

15/16 

11/16 

ij 

9/16 

3/8 

2! 

if 

I* 

li 

13/16 

if 

2 

5/8 
11/16 

13/32 
7/16 

2- 
2 

\ 

If 
2 

I* 

»x 

If 

15/16 

»£ 

21 

3/4 

15/32 

3 

!r 

2\ 

1« 

IT"* 

22 

13/16 

1/2  ' 

3| 

2| 

if 

i| 

'I6* 

2f 

7/8 

17/32 

3H 

2f 

Iff 

27V 

'TV 

BELT  GEARING. 


259 


260 


DRAWING   AND    DESIGNING. 


-A-l—'G- — i 


BELT  GEARING. 


26l 


Exercise  89. — Make  a  drawing  of  the  rope  pulley  rim  section 
shown  in  Fig.  182.      Diam   of  rope  to  be  ij"     Scale  full  size. 
Remaining  dimensions  may  be  taken  from  Table  34. 


TABLE  34. 

(Dimensions  in  inches.) 


D 

A 

B 

c 

£ 

£ 

C 

H 

/ 

I 

If 

2 

3/8 

1/2 

'  9/16 
5/8 
3/4 

if 

2f 

l£ 

| 

1/4 
5/i6 
3/8 
7/i6 

1/2 

3/4 
15/16 

I 

7/8 

1 

1 

3fl 

7|5 

2i 
2k 

7/8 
15/16 

3 

^I 

9/16 

5/8 

1 

2 

7!: 

Qf5 

2f 

I 

4 

11/16 

2| 

9H 

CHAPTER   VIII. 
TOOTHED   GEARING. 

PROPORTIONS  OF  IRON  TEETH.     Fig.  183. 


/  =  circular  pitch  =  k 

p'  =  diametral  pitch  (/  X  /')  =  3.1416; 
D  =  pitch  diameter  =  T  '-f-  p'  '  ', 

T  =  number  of  teeth  =  D  X  /  ; 

/=  addendum  of  tooth  =  .^p\ 

I'  =  flank  of  tooth  =  .35^  to  .4/5 

t  =  thickness  of  tooth  =  .48^  for  cast-iron  teeth, 

=  -5/  for  cut  teeth; 
k  =  .04  for  hand-wheels, 
=  .05  for  ordinary  mill  gears, 

=  .06  for  wheels  of  high  velocity  and  mortise  gearing; 
P  =  the  total  force  transmitted  by  one  wheel  to  another 

through  a  corner  of  the  tooth  =  —  7^—  =  63020-^^; 
V  •=•  the  velocity  of  the  pitch  line  in  feet  per  second 


R=  the  radius  of  the  pitch  circle  in  inches; 

7V=  the  number  of  revolutions  of  the  wheel  per  minute; 

H  =•  the  horse-power  transmitted  by  the  wheel. 


262 


TOOTHED    GEARING. 


263 


WOOD  TEETH  or  cogs  for  mortise  wheels  are  usually  made 
thicker  than  for  the  iron  teeth  of  the  meshing  wheel. 

/'  =  thickness  of  iron  teeth  to  mesh  with  mortise  wheel 

=  -4/; 

t  =  thickness  of  wood  cog  =  .6/. 

Exercise  90.  (Fig.  183.) — To  construct  the  teeth  for  a  spur 
gear  of  15  teeth  and  rack,  p'  or  diametral  pitch  =  2.5. 
Involute  system,  angle  of  action  =  15°. 

Draw  the  centre  line  C,  and  compute  the  diameter  of  the 
pitch  circle  by  dividing  the  number  of  teeth  by  p' . 

At  the  point  a  where  the  pitch  circle  cuts  C  draw  line  L, 
making  an  angle  of  15°  with  the  horizontal  pitch  line,  and 
draw  the  base  circle  tangent  to  L. 


FIG.  183. 


To  find  /:  Divide  360°  by  the  number  of  teeth:  the 
quotient  will  be  the  number  of  degrees  in  the  arc/,  which 
may  be  laid  off  with  a  protractor.  Or  divide  the  number  of 
inches  in  the  circumference  of  the  pitch  circle  by  the  number 
of  teeth  :  the  quotient  will  be  the  pitch.  Or  divide  a  quadrant 


264  DRAWING   AND   DESIGNING. 

of  the  pitch  circle  with  the  hair-spring  divider  into  15  equal 
parts,  and  from  the  point  a  mark  every  fourth  division  for 
the  point  where  the  outline  of  a  tooth  intersects  the  pitch 
circle.  Next  lay  off  the  thickness  of  the  tooth  equal  to  half 
the  pitch  on  the  pitch  circle  of  the  wheel  and  the  pitch  line 
of  the  rack. 

Draw  the    addendum   line    of   the   wheel   with   a   radius 


The  root  line  of  the  rack  is  drawn  tangent  to  the  adden- 
dum line  of  the  wheel,  and  the  root  line  of  the  wheel  is 
tangent  to  the  addendum  line  of  the  rack. 

To  describe  the  involute  curve  of  the  wheel-tooth  :  Take  a 
piece  of  tracing-paper  or  thin  celluloid,  and  trace  upon  it  the 
straight  line  L,  and  make  a  small  puncture  at  the  point  a  with 
a  needle.  Now  at  the  point  where  line  L  is  tangent  to  the 
base  line  stick  a  needle,  and  rotate  line  L  about  it  counter- 
clockwise until  it  intersects  the  base  line  ;  at  the  point  of  in- 
tersection stick  another  needle,  and,  removing  the  first  needle, 
adjust  the  tracing  until  the  line  L  becomes  tangent  to  the 
base  line  at  the  second  needle;  then  through  the  puncture  a 
in  the  tracing,  with  a  4.H  pencil  sharpened  to  a  conical  point 
mark  -a  point  on  the  drawing-paper:  this  will  be  a  point  on 
the  curve.  Continue  to  find  similar  points  until  a  sufficient 
number  has  been  found  to  form  the  addendum  of  the  tooth. 

It  will  be  seen  by  the  figure  that  the  involute  curve 
forming  the  addendum  of  the  tooth  extends  below  the  pitch 
line  to  the  base  line;  this  part  of  the  curve  is  generated  in  a 
similar  way  to  the  part  above  the  pitch  line,  except  that  the 
generating  line  L  must  be  rotated  in  the  opposite  direction. 


TOOTHED    GEARING. 


265 


The  addendum  lines  of  the  other  teeth  may  be  traced 
from  the  one  just  found. 

The  rim  of  the  rack,  according  to  Reuleaux,  should  not 
be  less  than  S  in  thickness,  =  .^p  +  .125.  Unwin  gives 
.48/5  Low  &  Bevis  give  -47/.  Use  Unwin's  proportion. 

When  the  curves  have  been  carefully  pencilled  as  above, 
they  may  be  inked  in  with  arcs  of  circles  computed  by  means 
of  the  following  odontograph  table,  taken  from  Geo.  B. 
Grant's  "  Handbook  on  the  Teeth  of  Gears" : 


ODONTOGRAPH    TABLE— INVOLUTE  TEETH. 

CORRECTED    FOR    INTERFERENCE,    INTERCHANGEABLE    SET. 


Teeth. 

Divide  by  the  Diametral 
Pitch. 

Multiply  by  the  Circular 
Pitch. 

Face 
Radius. 

Flank 
Radius. 

Face 
Radius. 

Flank 
Radius. 

12 

2.70 

•83 

.86 

.27 

13 

2.87 

•93 

.91 

•30 

14 

3-00 

1.  02 

•95 

•33 

15 

3-15 

1.  12 

.00 

.36 

16 

3-29 

1.22 

•05 

.40 

17 

3-45 

•31 

.09 

•43 

18 

3-59 

.41 

.14 

.46 

19 

3-71 

•53 

.18 

•50 

20 

3.86 

.62 

.22 

•53 

21 

4.00 

•73 

.27 

•57 

22 

4.14 

•83 

•32 

.60 

23 

4.27 

•94 

•36 

.63 

25 

4-56 

2.15 

•45 

.70 

28 

4.82 

2.37 

•54 

•77 

31 

5-23 

2.69 

.67 

.88 

34 

5-77 

3.13 

1.84 

1.  00 

38 

6.30 

3-58 

2.01 

1.16 

44 

7.08 

4.27 

2.26 

1.38 

52 

8.13 

5-20 

2-59 

1.70 

64 

9.68 

6.64 

3-09 

2.18 

83 

12.  II 

8-93 

3-87          ' 

2.90 

US 

16.18 

12.80 

5-16 

4-15 

200 

25.86 

22.30 

8.26 

7.30 

266 


DRAWING  AND   DESIGNING. 


For  any  intermediate  number  of  teeth  proportionally 
intermediate  values  can  easily  be  found  by  calculation. 

Example. — A   gear-wheel  has   30  teeth,  and   the   nearest 

5.23  X  30 
number  of  teeth  in  the  table  is'  31;  then =  5.06, 

the  number  to  be  divided  by/7  (1.25),  making  the  true  face 
radius  —  4^"  nearly. 

The  flank  of  the  tooth  is  radial,  and  it  is  joined  to  the  rim 
with  a  fillet  whose  radius  is  equal  to  the  clearance. 

A  special  rule  is  provided  for  the  rack-teeth:  the  flank 
and  one  half  the  face  is  a  straight  line  drawn  at  right  angles 
to  line  L ;  the  other  half  of  the  face  is  a  circular-arc  centre 
on  the  pitch  line  and  a  radius  found  by  dividing  2.10"  by/'. 

This  rounding  of  the  point  of  the  rack-tooth  is  necessary 
when  it  is  to  mesh  with  a  pinion  having  less  than  28  teeth. 

The  following  tables  will  be  found  convenient  for  compar- 
ing the  diametral  pitch  with  the  circular  pitch ;  they  are 
from  Grant's  "Teeth  of  Gears": 


Cir. 

Pitch. 

Diam. 
Pitch. 

6 

•52 

5i 

•58 

5 

•63 

4* 

.70 

4 

.78 

3s 

.90 

3 

•05 

2I 

•15 

2f 

•25 

4 

.40 

2 

•57 

if 

.80 

ij 

2.10 

ii 

2.50 

i      • 

3-14 

f 

4.2O 

1 

6.28 

Diam. 
Pitch. 

Cir. 

Pitch. 

i 

6.28 

i 

4.20 

i 

3-14 

i^ 

2.50 

i^ 

2.IO 

it 

1.  80 

2 

1-57 

2I 

1.25 

3 

1.05 

3i 

.90 

4 

.78 

5 

•63 

6 

•52 

7 

•45 

8 

•39 

9 

•35 

10 

•3i 

TOOTHED    GEARING.  26? 

Exercise  91.  (Fig.  184.)—  To  construct  the  teeth  for  a 
spur-gear  wheel  and  pinion  ;  wheel  to  have  40  and  the  pinion 
12  teeth.  /'  =  2.10.  Walker  system,  non-interchangeable. 


FIG.  184. 

The  curves  of  the  teeth  are  epicycloids  and  epitrochoids, 
and  are  found  by  rolling  the  pitch  circles  on  each  other  as 
follows :  For  the  addendum  of  the  wheel-teeth  draw  arc  A 
on  a  piece  of  tracing-paper  or  celluloid,  and  place  it  over  the 
drawing  tangent  to  arc  B  at  the  point  a.  Through  the 
point  a  on  the  celluloid  make  a  puncture  with  a  needle,  and 
while  holding  the  needle  at  a  rotate  the  celluloid  a  small 
distance  to  the  right  until  arc  A  intersects  arc  B.  At  the 
point  of  intersection  place  another  needle,  and,  removing  the 
first  needle,  adjust  the  celluloid  so  as  to  make  arc  A  tangent 
to  arc  B  at  the  second  needle,  and  through  the  puncture 
mark  a  point  with  the  pencil ;  this  will  be  a  point  in  the 
curve  of  the  face  edge.  Other  points  may  be  found  in  a 
similar  way  to  complete  the  curves  required. 

For  the  face  edge  of  the  pinion-tooth  roll  arc  B  on  arc  A, 
and  the  point  a  will  describe  the  curve  ab. 


268 


DRAWING  AND   DESIGNING. 


To  draw  the  flank  of  the  wheel-tooth :  When  arc  A  on 
the  celluloid  is  tangent  to  arc  B  at  a,  trace  curve  ab  on  the 
celluloid  and  make  a  puncture  through  b\  then  roll  arc  A  to 


the  lett  on  B,  and  point  £  will  describe  the  flank  of  the  tooth. 
The  flank  of  the  pinion-tooth  is  then  found  by  rolling  arc  B 
on  arc  A,  when  the  point  b'  wiil  describe  the  curve. 


TOOTHED    GEARING.  269 

Exercise  92.  (Fig.  185.) — Draw  the  HALF  ELEVATION, 
HALF  PLAN,  and  HALF  SECTIONAL  PLAN  of  a  spur-gear  wheel 
and  pinion  ;  the  wheel  to  have  60  and  the  pinion  15  teeth. 

/=2.5. 

Draw  all  the  teeth  in  one  quadrant  of  the  elevation, 
involute  system.  Fig  185  is  the  drawing  of  a  spur-gear 
wheel  made  by  Messrs.  Robert  Poole  &  Sons  of  Baltimore, 
Md.,  and  presented  to  Sibley  College  for  use  as  a  model  in 
the  drafting-room. 

Exercise  93.  (Fig.  186.) — Draw  ELEVATION,  CROSS-SEC- 
TION, and  PLAN  of  a  bevel-gear  wheel  and  pinion.  The  axes 
are  to  be  at  right  angles  to  each  other,  and  the  wheel  is  to 
have  50  and  the  pinion  24  teeth,  p'  =  2.10.  Radial  flank 
system,  non-interchangeable. 

Draw  centre  lines  C  and  C'  at  right  angles  to  each  other, 
find  the  radii  of  the  pitch  circles,  and  draw  D  and  D'  at  the 
proper  distance  from  the  axes.  Draw  E  and  E'  at  right 
angles  to  each  other.  F  and  F'  are  the  developed  pitch 
circles  on  which  the  teeth  are  drawn,  the  same  as  if  they  were 
for  spur  gears.  And  since  the  flanks  are  radial,  the  rolling 
circles  A  and  B  used  to  generate  the  face  curves  of  the  teeth 
are  equal  in  diameter  to  the  radius  R  and  R!  of  the  developed 
pitch  circles  of  the  pinion  and  wheel  respectively. 

A  model  of  this  wheel  will  be  found  in  the  drafting-room 
for  use  in  connection  with  this  problem. 

Exercise  94.  (Fig.  187.)  —  Construct  a  worm-wheel  and 
worm  ;  the  wheel  to  have  50  teeth,  and  the  worm-teeth  to  be 
drawn  like  those  of  the  involute  rack ;  that  is,  the  face  edge 
will  be  drawn  at  right  angles  to  line  Ly  when  line  L  makes 


270 


DRA  WING   AND    DESIGNING. 


the  angle  of  15°  with  the  horizontal  pitch  line  H,  as  shown 

c~ 

by  the  longitudinal  cross-section  in  Fig.  187. 

The  teeth  of  the  wheel  are  made  by  a  cutter  similar  to 


the  worm,  except  that  grooves  are  cut  in  the  threads  parallel 
f    to  the  axis,  and  the  material  is  hardened  steel.     The  worm 
itself  is  usually  made  of  cast  iron,  but  is  sometimes  made  of 
wrought  iron  or  malleable  cast  iron. 


TOOTHED    GEARING. 


271 


The  horizontal  pitch  line  should  be  so  placed  as  to  bisect 
the  cross-sectional  area  of  the  wheel-tooth  at  a;  otherwise 
the  proportions  of  the  teeth  may  be  the  same  as  those  used 
for  wheel  and  rack. 


FIG.  187. 


Exercise  95.  (Fig.  188.)  —  Design  a  cast-  iron  gear-  wheel 
given  the  pitch-circle  diameter  51",  revolutions  per  minute  90, 
horse-power  transmitted  280. 

First  find  the  wnole  pressure  of  one  wheel  on  the  other 


=  P  = 


;  (V=  .00873^^  =  .00873  X  25.5  X  9°0  then 


find  the  circular  pitch  /  =  .0447 

*~  The  number  of  teeth  can  now  be  found  by  multiplying 

the  diameter  of  the  pitch  circle  D  X  3.1416,  and  dividing  by 

51  X  3.1416 
p  =  -  -  =  the  nearest  even  number. 


272 


DRAWING   AND    DESIGNING. 


FIG.  188. 


Let  T  represent  the  number  of  teeth ;  then  the  velocity 
of  the  pitch  line  may  be  expressed  as  follows: 


- 
12  X  1 6' 


and  the  pressure  on  the  teeth  is 


550  X  12  X  6o  X  H  H 

-  =  396000 


pTN 


pTN 


TOOTHED    GEARING.  2/3 

Taking  the  width  of  the  teeth  into  consideration,  let 
t  =  .$6p  for  iron  teeth  when  worn, 

=  .45/  for  wood  teeth  when  worn  ; 
h  =  .Jp  for  iron  teeth, 

=  .6p  for  wood  teeth;  then 

P=  .O46£//for  iron  teeth, 
=  .o84^//for  wood  teeth; 


and  /  =  £,A  fj-  VP  when  b  =  width  of  tooth  =  from  2  to 
and  in  practice 


ki  =  .0707  for  iron  wheels, 
=  .0848  for  mortise  wheels. 

When  b  =  2.5/,  Unwin  gives/  =  .0447  VP 


Low  &  Bevis  give/  =  \  / =. 

v    2OO  JL 


The  dimensions  of  the  teeth  may  be  determined  from 
the  proportions  already  given :  b  =  the  breadth  of  face 
"=  2.5/,  etc. 

As  the  shaft  for  this  wheel  would  probably  have  to  resist 
a  combined  twisting  and  bending  action,  we  can  assume  the 
diameter  of  the  shaft  to  be  6",  and  the  wheel  fit  j" . 

The  width  and  breadth  of  the  arms,  the  thickness  of  the 
rim,  and  the  thickness  and  length  of  the  hub,  etc.,  can  be 
easily  determined  by  the  proportions  given  in  the  following 
pages. 


274 


DRA  WING   AND    DESIGNING. 


Arms  of  Gear  Wheels.  —  The  usual  shapes  of  arm  cross- 
sections  are  shown  in  Figs.  189  to  192.  Fig.  189  is  mostly 
used  for  pulleys  and  light  wheels;  Fig. 
191  shows  another  section  that  is  com- 
monly used  in  light  spur  wheels,  that  in 
Fig.'  192  for  heavy  spur  gears,  and  that 
in  Fig.  189  for  bevel  gears. 

When    a  =  .48^  =  the    thickness    of 


__ 
the    teeth,    Unwin  gives  h  —  -^  VbRy 

Vn 

measured  at  the  centre  of  the  wheeh 
Taper  J"  in  12"  on  each  side  toward 
the  rim.  n  =  the  number  of  arms;  R  = 
the  radius  of  the  wheel;  b=  the  width 
of  the  cross-feathers,  which  may  be  = 
the  breadth  of  the  teeth  as  shown  at  b 
in  Fig.  193,  or|-  the  breadth  of  the  teeth 
measured  at  the  centre  of  the  shaft  and 
from  f  to  |f  at  the  rim. 

The  ribs  or  feathers  B  do  not  add 
much  to  the  resistance  of  the  arms  to 
bending  in  the  direction  of  the  driving 
force,  but  they  are  necessary  to  give  lateral  stiffness  to  the 
arms.  Unwin  gives  B  =  .$p.  The  feathers  should  be 
tapered  to  facilitate  the  removal  of  the  pattern  from  the 
sand. 

To  determine  the  number  of  arms  in  a  wheel,  Low  &  Bevis 

give  '—2  +  4-     The  nearest  number  divisible  by  2  should  be 
taken. 


TOOTHED    GEARING. 


275 


Unwin  gives  four  arms  for  wheels  not  over  4  ft.  in 
diameter,  six  arms  for  wheels  of  from  4  to  8  ft.  in  diameter, 
and  eight  arms  for  wheels  from  8  to  16  ft.  in  diameter. 

Rims  of  Gear  Wheels.— The  usual  rim  sections  are 
shown  in  Figs.  193  to  204.  The  section  shown  in  Fig.  193 
is  commonly  used  in  light  wheels. 

The  following  proportions  agree  closely  with  most  au- 
thorities on  the  subject:  d=  the  thickness  of  the  rim  at  the 
edge  =  .48/>.  The  other  proportions  are  shown  in  the 
figures. 

In  the  rims  for  bevel  gears  shown  in  Figs.  198  to  200 
the  thickest  part  of  the  rim  should  be  \d. 

Figs.   20 1   and  202  show  examples  of  mortise  gears  for 


FIG.  197. 


FIG.  198. 


FIG.  199. 


spur  and  bevel  wheels  respectively;  the  mortise  teeth  are 
fixed  either  by  wood  keys  as  shown  in  Fig.  201,  or  by 
round  iron  pins  as  shown  in  Fig.  202.  The  proportions 
given  in  the  figures  agree  closely  with  good  practice. 


DRAWING   AND   DESIGNING. 

Shrouding. — When  the  rim  of  a  wheel  is  wider  than  the 
teeth  and  extends  towards  the  point  so  as  to  form  an  annular 
ring  uniting  the  ends  of  the  teeth,  the  teeth  are  said  to  be 
shrouded.  Figs.  203  and  204  give  two  examples  of  shrouded 
teeth.  By  shrouding  out  to  the  pitch  circle  as  shown  in 
Fig.  203,  teeth  which  are  no  thicker  at  the  root  than  at  the 
pitch  circle  can  be  strengthened  about  100  per  cent.  In  the 
pinion  of  a  pair  of  gear  wheels  the  shrouding  may  extend  to 
the  points  of  the  teeth  as  shown  in  Fig.  204;  this  compen- 
sates for  the  weak  form  of  the  teeth  in  very  small  wheels,  and 
prevents  their  failure  from  excessive  wear. 


FIG.  201. 


FIG.  203 


FIG.  204. 


Hubs  of  Gear  Wheels. — Figs.  205,  206,  and  207  give 
examples  of  hubs  to  correspond  to  the  examples  of  arms 
shown  in  Figs.  189,  191,  and  192,  respectively. 

The  thickness  of  metal   surrounding  the  bore  of  a  gear 


TOOTHED    GEARING. 


277 


wheel  is  given  by  Reuleaux  =  w  =  .4/1  +  .4"  (when  h  =  the 
width  of  the  arm  measured  at  the  centre  of  the  wheel).  The 
keyway  should  be  cut  the  full  length  of  the  hub,  and  the 
metal  reinforced  over  the  keyway  if  the  wheel  is  in- 
tended for  heavy  duty.  In  large  wheels  the  hubs  are 
sometimes  strengthened  by  wrought-iron  rings  shrunk  on 


w 


both  ends;  the  thickness  is  made  =  — ,  and  the  thickness  of 
the  metal  under  the  rings  is  \w.     b  =  width  of  teeth. 


FIG.  205. 


FIG.  206. 


FIG.  207. 


In  heavy  wheels  with  a  large  amount  of  metal  surround- 
ing the  bore,  the  hub  is  sometimes  slotted  across  between 
the  arms  to  give  relief  from  initial  strains  due  to  unequal 
contraction  in  cooling;  these  slots  are  then  filled  with  metal 
strips,  and  the  divided  hub  is  held  firmly  together  by  the  iron 
or  steel  ring  referred  to  above. 


OF  THE 

UNIVERSITY 


CHAPTER  IX. 
VALVES,  COCKS,  AND  OIL-CUPS. 

Valves. — A  valve  is  a  device  for  regulating  the  flow  of  a 
fluid  through  an  opening. 

Prof.  Unwin  divides  valves  into  three  classes: — (i)  Flap- 
valves,  or  those  which  open  with  a  hinge ;  (2)  lift-valves,  or 
those  which  rise  perpendicularly  to  the  seat ;  (3)  slide-valves, 
or  those  which  move  parallel  to  seat.  The  valve-face  is  that 
part  of  the  valve  in  contact  with  its  seat  when  closed. 

Foot-valve  and  Strainer. — Foot-valves  are  used  to  hold 
the  water  in  long  suction-pipes;  otherwise  the  pump  would 
have  to  be  charged  every  time  before  starting. 

The  strainer  protects  the  valve  from  being  choked  with 
stones  or  other  solids.  The  most  common  foot-valves  are 
made  of  two  cast-iron  boxes,  called  the  valve-box  and  strainer, 
bolted  together  by  flanges,  and  having  a  leather  clack-valve 
between  them.  The  lower  box  is  perforated  with  circular 
holes  y  to  y  diameter,  and  is  called  the  strainer  or  snore- 
piece.  In  small  foot-valves  the  suction  is  generally  screwed 
into  the  top  of  the  valve-box. 

Fig.  207  shows  a  vertical  section  and  three  half  plans  of  a 
foot-valve  for  a  9"  suction-pipe.  VB  is  the  valve-box,  5  the 

strainer,  A  is  the  valve-seat,  B  main  valve,  and  C  an  auxiliary 

278 


VALVES,    COCKS,  AND    OIL-CUPS. 


279 


FIG.  207. 


280  DRAWING   AND   DESIGNING. 

valve  on  top  of  B.  This  style  of  clack  is  called  a  relief  or 
break  clack.  Mr.  Henry  Teague,  of  Lincoln,  England,  in  a 
paper  read  before  the  Inst.  of  M.  E.  of  England,  in  1887, 
reported  having  used  a  15"  main  clack  with  a  5"  supple- 
mentary clack  for  the  purpose  of  reducing  the  very  great  con- 
cussion which  was  had  by  using  the  15"  clack  alone,  with  the 
result  that  even  when  the  hand  or  the  ear  was  placed  on  the 
clack-box  hardly  a  tremor  or  a  sound  was  perceptible.  D  is 
the  entrance  to  the  suction-pipe. 

This  double-valve  feature  gives  almost  complete  freedom 
from  shocks  even  in  large  pumps,  and  therefore  works  very 
quietly. 

The  main  valve,  made  of  £"  leather,  forms  the  joint  be- 
tween the  valve-box  and  the  strainer.  E  is  the  top  and  F  is 
the  bottom  valve-plate,  riveted  together  with  f-inch  rivets, 
and  an  opening  in  the  centre  equal  to  an  area  of  about  one 
half  or  one  third  that  of  the  main  opening.  This  auxiliary 
opening  is  fitted  with  the  clack-valve  C  referred  to  above. 
It  has  an  upper  and  a  lower  valve-plate,  held  together 
with  the  bolt  H  and  fastened  to  the  main  valve  with  two 
screws  at  X,  in  plan  and  sectional  elevation. 

The  laps  L  should  be  made  one  tenth  of  the  diameter  of 
the  respective  valve-openings. 

Exercise  96. — Make  drawings  of  foot-valve  and  strainer 
shown  in  Fig.  207,  and  also  an  outside  elevation  of  the  valve- 
box  and  strainer.  Scale  3"  =  i  foot. 

India-rubber  Valve. — This  valve  (Fig.  208)  consists  of  an 
india-rubber  disk  D,  a  brass  grating  or  seat  s,  and  a  perfo- 
rated brass  guard.  The  rubber  guard  and  valve  are  attached 
to  the  grating  by  a  stud-bolt  B.  The  purpose  of  the  guard 


VALVES,    COCKS,   AND    OIL-CUPS. 


28l 


FIG.  208. 


282 


DRAWING  AND   DESIGNING. 


FIG.  209. 


VALVES,    COCKS,   AND    OIL-CUPS.  283 

is  to  prevent  the  valve  from  rising  too  high.  The  perforations 
in  the  grating  should  not  be  large  enough  to  cause  much 
flexure  of  the  rubber  disk.  The  area  of  the  grating  should  be 
such  that  when  the  valve  is  closed  the  pressure  does  not  ex- 
ceed 40  Ibs.  per  square  inch. 

The  thickness  of  the  india-rubber  disk  for  large  valves — 
i.e.,  valves  over  6"  in  diameter — in  cqndensers  and  pumps 
should  be  f"  to  -J".  India-rubber  valves  are  not  good  for 
pressures  over  100  Ibs.  per  square  inch. 

Exercise  97. — Make  a  complete  drawing  of  the  india-rubber 
valve  as  shown  in  Fig.  208.  Scale  f  Jill  size.  The  projection 
of  the  perforations  in  the  conical  guard  is  shown  in  Fig.  209. 

The  following  proportions  represent  good  practice.  Use 
the  nearest  TV'.  Unit  =  .  19  \/^ 

a  =  diameter  of  india  rubber  disk  =15.5  of  unit. 

b  =  thickness  of  the  india-rubber  disk  =     1.6       " 

c  =  thickness  of  the  grating-lip  =     1.75     " 
d=  diameter  of  the  valve. 

e  =  depth  of  seat-body  =    2.75 

y  =  diameter  of  stud-body  =    2.75 

g  =  diameter  of  stud  =     1.75 

h  =  diameter  of  holding-down  bolt  =•    1.25 

k  =  depth  of  grating  =2.50 

/  =  thickness  of  grating-rib  =       .65    " 

m  =  width  of  seat-lip  =       .75    " 

n  =  diameter  of  guard  =  12.00    " 

Exercise  98. — Make  a  complete  drawing  of  an  india-rubber 
disk-valve  similar  to  Fig.  208.  d  =  10".  Scale  9"  =  i  foot. 


" 


i . 


284 


DRA  WING   AND   DESIGNING. 


FIG.  210. 


VALVES,    COCKS,   AND    OIL-CUPS.  28$ 

Lift-  or  "Wing-valves  (Fig.  210). — These  valves  are  usu- 
ally made  of  brass.  The  essential  features  are  a  circular  disk 
and  seat.  The  edges  between  the  disk  and  seat  are  bevelled 
to  the  angle  of  45°,  and  are  easily  fitted  and  ground  together. 
Springs  or  rods  are  used  to  close  these  valves  when  it  is  neces- 
sary to  place  them  in  a  horizontal  position.  To  give  the  valve 
a  partial  rotation  and  provide  a  new  seating  at  each  stroke  the 
wings  are  curved  slightly,  as  shown  at  Fig.  21 1.  The  curving 
is  arbitrary,  and  may  be  projected  as  showr  in  the  figure. 
The  outside  of  the  seat  has  usually  a  taper  of  J"  in  12",  but 
is  sometimes  driven  straight.  The  amount  of  the  lift  of 
the  valve  may  be  determined  as  follows : 

Let 

a  =  area  of  opening  in  seat ; 
d  =  diameter  of  opening  in  seat; 
L  =  lift  of  valve. 
Then 

a  =  .7854^'  and  L  =  .35^. (l) 

Taking  a  unit  of  proportion  =  .2  V^~then 

«•  ==  thickness  of  disk  =  1.3 ; 

/  =  length  of  wings  =  8 ; 

/  =  thickness  of  seat  =  i  at  small  end. 

Exercise  99. — Draw  the  valve  as  shown  in  Fig.  210  to  the 
dimensions  given.  Scale  full  size. 

Exercise  100. — Make  drawing  of  the  curved  wing-valve  as 
shown  in  Fig.  211.  Scale  full  size. 

Spindle-valves  (Fig.  212).— These  valves  are  guided  cen- 
trally by  means  of  a  spindle  and  bridge ;  otherwise  they  are 


286 


DRAWING   AND    DESIGNING. 


r 


FIG.  211, 


VALVES,    COCKS,   AND   OIL-CUPS. 


FIG.  212. 


288  DRAWING   AND   DESIGNING. 

similar  to  the  wing-valve,  but  used  for  light  work  in  pumps. 
The  wing-valve  and  the  spindle-valve  are  sometimes  made  with 
a  flat  seat  and  a  leather  face  and  also  used  for  light  duty  in 
pumps,  but  have  no  advantage  over  the  bevelled  metal  edges. 
Let  W(Fig.2  io)  =  the  width  of  the  bearing-edges  measured 
perpendicularly  to  the  axis  of  the  valve,  /  =  the  maximum  dif- 
ference of  pressure  on  the  two  sides  of  the  valve ;  then  „,  = 

the  crushing  pressure  per  square  inch  on  the  narrow  bevelled 
edges  of  the  valve  and  seat. 

The  greatest  safe  pressure  per  square  inch  for  phosphor- 
bronze  is  3000  Ibs. ;  for  gun-metal,  2000  Ibs.  ;  cast  iron, 
1000  Ibs.  ;  and  leather  and  india-rubber,  700  Ibs. 

Exercise  101. — Make  drawings  of  the  spindle  and  valve  as 
shown  in  Fig.  212.  Scale  full  size. 

Ball-valves  (Fig-  213). — These  valves  are  much  used  in 
deep  well-pumps  and  small  fast-running  pumps.  To  guide 
the  lift  of  the  ball  it  is  surrounded  by  a  cage  with  three  or 
four  ribs.  The  ribs  should  be  as  narrow  as  safety  will  per- 
mit, so  as  not  to  interfere  with  the  free  flow  of  the  fluid  above 
the  valve-seat.  Gun-metal  is  the  best  material  for  the  balls. 
To  lighten  them  they  should  be  made  hollow. 

The  usual  proportions  for  the  ball-valves  are  given 
below: 

Unit  =  .2  V~d. 

a  =  diameter  of  ball  =  I.34*/. 

b  =  inside  diameter  of  seat-casing  =  \.\2d. 

c=  thickness  of  ball-guide  =  .9  times  unit. 

e  =  distance  between  guides  =  a  -f-  iV'- 


VALYES,    COCKS,   AND    OIL-CUPS. 


289 


FIG.  213. 


290 


DRAWING   AND   DESIGNING. 


f=  length  of  seat-shank 

g  =  thickness  of  seat-flange 

h 

k 

I  =  lift  of  valve 

/  =  thickness  of  ball-shell 


=  3  times  unit. 

=  i 

=  1.2          " 

=  1.8 


=  1.2 


These  valves  work  best  with  a  small  lift.      William  M.  Barr 
says  that  the  lift  of  ball-valves  should  not  exceed  i". 

Exercise  102.  —  Make  drawings  similar  to  those  shown  in 


Fig.  213.     d  =  i 


Scale  i%  full  size. 


Flat  India-rubber  Disk-valves.  —  Fig.  2  14  shows  an  ordi- 
nary example  of  this  style  of  valve  for  cold  water.  The 
valve-seat  and  spindle  are  cast  in  one  piece.  The  spindle  is 
turned  and  polished,  and  the  hole  in  the  india-rubber  cftsl^  is 
Ty  larger  than  the  diameter  of  the  spindle.  This  allows  free 

action  of  the  valve.      The  valve-seat  is  screwed  into  place  with 

r    < 

a  pitch  of  eight  threads  to  the  inch,  which  may  be  maintained 
for  all  sizes  up  to  4^''  diameter.  Mr.  W.  M.  Barr  gives  the 
following"  dimensions  for  india-rubber  valves  : 

TABLE   35. 


Diameter. 

Thickness. 

Hole. 

2" 

r 

i" 

2^" 

r 

3" 

Tr  -    - 

TV 

3*" 

i;;. 

6" 

4" 

f 

1 

if" 

Springs  give  good   results  if  made  with  No.  12  brass  wire 
for  2"  and  2\"  valves;  No.  10  wire  for   3"  and  3^"  valves, 


VALVES,    CCCKS,    AND    OIL  CUPS. 


29I 


I 


FIG.  214. 


292  DRAWING   AND   DESIGNING. 

and  No.  8  for  4"  and  4J-  valves.  The  outside  diameter  of  the 
spring  may  be  —  .5  that  of  the  valve-disk.  Five  to  six  coils 
will  give  a  suitable  elasticity. 

Exercise  103. — Make  drawings  for  the  india-rubber  flat-disk 
valve,  as  shown  in  Fig.  214,  to  the  dimensions  given.  Scale 
full  size. 

Globe -valves. — These  valves  are  opened  and  closed  by 
hand.  The  valve  in  Fig.  2  14  is  for  steam.  When  such  a  valve 
is  used  for  cold  water  the  valve-face  is  made  of  leather  or 
india-rubber,  and  when  for  hot  water  the  india-rubber  is 
mixed  with  graphite. 

The  construction  of  the  valve  is  so  plainly  shown  in  Fig. 
215  that  a  description  seems  unnecessary. 

Exercise  104. — Make  drawings  of  globe-valve  as  shown  in 
Fig.  215,  and  also  a  right-end  elevation.  Scale  full  size. 

Stop-valve  (Fig.  216). — This  is  another  style  of  lift-valve 
controlled  by  hand.  The  particular  valve  shown  in  the  figure 
is  used  as  a  throttle-valve  by  the  Ball  Engine  Co.,  who  kindly 
sent  drawings. 

Let 

/  =  thickness  of  casing; 
/  =  pressure  in  Ibs.  per  square  inch ; 
d=  diameter  of  the  sphere  in  inches; 
/—  safe  bursting  strength  of  material. 

Take  2000  for  cast  iron  and  17,500  for  yellow  brass,  and 
use  a  factor  of  safety  8,  which  gives  2500  for  the  former 
and  about  2200  for  the  latter;  then 


_ 

4/ 


VALVES,    COCKS,    AND    OIL- CUPS. 


293 


rr 

--// 1 


Fro.  215. 


294 


DRAWING  AND   DESIGNING. 


F-'H 


FIG.  216. 


VALVES,    COCKS,   AND    OIL-CUPS. 

The  lift  of  the  valve  may  be  determined  by  formula  (i) 
for  winged  lift-valves.  The  valve  and  its  seat  must  pass 
through  the  valve-chest,  so  the  opening  should  be  made  about 
•J"  larger  than  the  outside  diameter  of  the  valve-seat. 

The  length  of  the  thread  on  the  valve-stem  is  equal  to 
the  length  of  the  nut  +  lift  of  valve  +  J"  for  clearance. 

Exercise  105. — Make  drawings  of  the  stop-valve  as  shown 
in  Fig.  216.  Scale  4."  =  I  foot. 

Make  the  diameter  of  the  inlet  6£"  to  the  root  of  the 
thread,  instead  of  6"  as  shown  in  the  figure. 

Boiler  Check-valve. — Fig.  '2 1 7  shows  working  drawings  of 
the  Foster  Safety  Boiler-check. 

Exercise  106. — Make  drawing  of  the  Foster  Boiler-check 
as  shown  in  Fig.  217.  Scale,  full  size. 

Cocks. — Cocks  are  valves  which  operate  with  a  rotary 
motion.  The  most  common  style  of  cock  is  that  which  con- 
sists of  a  plug  made  in  the  form  of  a  truncated  cone  rotating 
in  a  seat  of  the  same  shape  cast  on  a  pipe. 

In  Fig.  218  /*isthe  plug,  and  C  the  casing  or  conical  seat. 
O  is  the  opening  through  the  plug.  By  rotating  the  plug  in 
one  direction  the  openings  are  brought  in  line  with  the  inlet 
A  and  outlet  B  of  the  pipe  or  casing.  In  this  position  the 
cock  is  open.  Further  rotation  through  90°  in  either  direction 
will  bring  the  openings  in  the  plug  opposite  the  solid  parts  of 
the  casing  and  close  the  valve. 

Exercise  107. — Make  drawings  of  the  blow-off  cock  shown 
in  Fig.  218,  and  in  addition  to  the  views  given  make  a  half 
sectional  plan  and  half  sectional  end  view.  Scale,  full  size. 

In  Fig.  219  is  shown  a  blow-off  cock  which  is  really  a 
wing-valve,  opened  and  closed  by  a  piston  which  in  turn  is  op- 


296 


DRAWING   AND   DESIGNING. 


VALVES.    COCKS,   AND    OIL-CUPS. 


297 


298 


DRAWING  AND   DESIGNING. 


VALVES,    COCKS,    AND    OIL-CUPS. 


299 


crated  by  means  of  compressed  air.  The  wing- valve  V  is  held 
on  its  seat  by  the  steam-pressure  in  the  boiler.  When  com- 
pressed air  is  introduced  into  the  cylinder  C  through  the  pipe 
P  the  piston  is  pushed  against  the  valve,  opening  it  and  allow- 


ing  the  contents  of  the  boiler  to  blow  through  the  cock  into 
the  discharge-pipe  D. 

Exercise  108. — Make  complete  drawings  as  shown  in  Fig. 
219.  Scale,  full  size. 

Oil-cups. — There  are  many  forms  of  oil-cups.     Figs.  220 


300 


DRAWING   AND   DESIGNING. 


to  225  inclusive  show  the  construction  of  some  of  the  oil-cups 
used  in  the  locomotives  of  the  Lehigh  Valley  Railway. 

Fig.  220  is  one  of  the  simplest  forms  of  oil-cups.     The 
material  is  brass,  cast  in  one  piece.     When  charged,  the  reser- 


voir is  filled  with  waste  and  oil.     This  cup  is  used  on  the 
link-hanger. 

Fig.  22 1  shows  another  simple  form  of  oil-cup,  used  to  oil 
the  rocker-box  and  cross-head. 


VALVES,    COCKS,    AND    OIL-CUPS. 


301 


Fig.  222  is  a  drawing  of  the  oil-cup  for  the  main  rod,  front 
end;  cross-wires  prevent  the' waste  from  being  thrown  out. 

Fig.  223  shows  another  form  of  oil- cup  used  on  the  valve 
stem.     The  flow  of  the  oil  is  regulated  by  the  spindle  S,  and 


TO  BE  BRAZED 


the  duty  of  the  spring  is  to  hold  it  in  position.     This  is  made 
of  -jJj"  brass  wire  J"  long  when  unloaded. 

Fig.  224  gives  a  form  of  oil-cup  for  the  front  end  of  the 


302 


DRAWING  AND  DESIGNING. 


FIG.  224. 


VALVES,    COCKS,    AND   OIL-CUPS. 


303 


MILLE* 


1BTSDS. 


FIG.  225. 


304  DRAWING   AND   DESIGNING. 

main  rod  on  cross-head.  It  will  be  seen  that  in  this  case  the 
flow  of  the  oil  is  also  mechanically  controlled. 

Fig.  225  is  a  form  of  cup  used  on  the  guides.  The  flow 
of  the  oil  is  in  this  case  also  regulated  by  the  raising  or  the 
lowering  of  the  spindle  by  hand. 

Exercise  109. — Make  drawings,  as  directed  by  the  in- 
structor, of  one  or  more  of  the  oil-cups  illustrated  in  Figs. 
220  to  225  when  it  is  desired  to  fill  unoccupied  space  on  .draw- 
ing-paper. Scale,  full  size. 


CHAPTER    X. 
ENGINE   DETAILS. 

The  Plain  Slide-valve — The  construction  of  all  slide- 
valves  must  be  such  as  to  satisfactorily  meet  the  following  re- 
quirements: 

1.  To  admit  steam  to  one  end  only  of  the  cylinder  at  a 
time ; 

2.  To  allow  the  steam  in  the  cylinder  to  escape  from  one 
end  at  least  as  soon  as  steam  is  admitted  at  the  other  end ; 

3.  To  prevent  steam  from  entering  the  exhaust-port  from 
the  steam-chest. 

During  one  revolution  of  the  crank  there  are  four  princi- 
pal points  reached  and  passed  by  the  valve  in  the  course  of 
its  travel : 

1.  The /<?*#/  of  admission,  when  steam  begins  to  enter  the 
cylinder.      (See  Fig.  236,  Plate  I.) 

2.  T\\Q  point  of  cut-off,  when  steam  is  prevented  from  en- 
tering the  cylinder.     (See  Fig.  233,  Plate  I.) 

3.  The  point  of  exhaust,  when  steam  is  released  from  the 
cylinder.      (Fig.  235,  Plate  I.) 

4.  The  point  of  compression,  when  the  exhaust  is  closed. 
(Fig.  234,  Plate  I.) 

305 


3o6 


DRAWING   AND   DESIGNING. 


In  Fig.  226  is  given  a  longitudinal  section  of  a  plane  slide- 
valve,  and  also  of  the  valve-seat  5  of  the  cylinder.  The  valve 
is  shown  in  its  central  position,  X  and  Fare  the  steam-ports 
and  Z  the  exhaust-port.  The  valve-face  is  the  under  side  of 
the  valve  with  a  length  equal  to  F=  ;i"  +  2L. 

Outside  Lap,  or  simply  lap  is  the  darkened  portion  L  of 


FIG.  226. 

the  valve  which  overlaps  the  steam-port  when  the  valve  is  in 
its  central  position.  Lap  has  no  effect  on  compression  or 
exhaust,  but  it  hastens  the  cut-off,  prolongs  expansion,  and 
shortens  the  time  the  port  is  open. 

Inside  Lap,  the  smaller  darkened  portion  /  which  over- 
laps the  bridge  between  the  steam-  and  exhaust-ports,  pro- 
longs expansion,  hastens  and  increases  compression,  retards 


ENGINE  DETAILS.  30? 

the  exhaust,  but  does  not  affect  the  admission  or  point  of 
cut-off. 

The  Travel  of  the  valve  is  equal  to  twice  the  total  dis- 
tance it  moves  from  its  central  position  in  either  direction;  or 
if  the  arms  of  the  rocker  are  of  equal  lengths,  then  the  travel  of 
the  valve  is  equal  to  twice  the  eccentricity  of  the  eccentric. 
(See  "  Eccentric  and  Straps.")  It  is  also  equal  to  twice  the 
sum  of  the  width  of  the  steam-port  and  lap  plus  the  over- 
travel  if  any. 

The  Lead  Angle  is  the  angle  made  by  the  centre-line  of 
the  crank  with  the  centre-line  of  motion  of  the  engine  when 
the  crank  is  at  the  point  of  admission.  (See  Fig.  236,  Plate  I.) 

The  Lead  is  the  amount  which  the  valve  has  opened  the 
steam-port  at  the  beginning  of  the  stroke.  (See  Fig.  231, 
Plate  I.)  To  obtain  smooth  running,  increased  speed  should 
have  increased  lead,  and  when  the  lead  is  increased  every 
operation  of  the  valve  is  quickened. 

The  Angle  of  Advance  of  the  eccentric  is  the  number  of 
degrees  which  the  centre-line  of  the  eccentric  is  over  90° 
ahead  of  the  centre-line  of  the  crank  without  a  rocker,  and 
with  a  rocker  it  is  the  number  of  degrees  short  of  90°  behind 
the  crank.  The  first  case  is  illustrated  in  the  diagram  in 
Plate  II,  as  follows:  Let  AO  be  the  centre  of  the  crank,  CO 
a  line  90°  ahead  of  it,  and  OE  the  centre-line  of  the  eccentric. 
Then  COE  is  the  angle  over  90°  ahead  of  the  crank,  and  is 
therefore  the  angle  of  advance.  For  the  case  with  a  rocker 
let  AO  be  the  centre  of  the  crank  as  before,  and  OD  a  line 
90°  behind  it,  and  OF  the  centre-line  of  the  eccentric.  Then 
the  angle  DOFis  the  angle  short  of  90°  behind  the  crank,  and 
is  therefore  the  angle  of  advance. 


308  DRAWING   AND    DESIGNING. 

Inside  Clearance  is  the  opposite  of  inside  lap,  instead 
of  the  valve  overlapping  the  bridge  when  on  the  centre;  as 
shown  at  /  in  Fig.  226,  it  shows  a  clearance  between  the  in- 
side edge  of  the  valve  and  the  bridge.  Inside  clearance 
hastens  exhaust,  delays  compression,  but  has  no  effect  on  the 
cut-off  or  admission. 

Overtravel  is  the  distance  the  steam  edge  of  the  valve 
travels  after  fully  opening  the  port,  as  shown  in  Fig.  232, 
Plate  I.  It  increases  the  sharpness  of  the  cut-off,  retards 
compression,  and  gives  a  later  release. 

Cylinder  Clearance  is  all  that  space  between  the  faces  of 
the  piston  and  the  valve  when  the  piston  is  at  the  beginning 
of  the  stroke. 

Piston  Clearance  is  the  distance  between  the  piston  and 
the  cylinder-head.  This  clearance  is  to  prevent  the  piston 
from  striking  either  cylinder-head  when  the  brasses  on  the 
connecting-rod  wear  and  cause  lost  motion. 

Point  of  Cut-off  is  the  point  on  the  crank-circle  which 
the  centre  of  the  crank  reaches  when  the  valve  cuts  off  the 
live  steam  from  the  cylinder,  and  for  the  remainder  of  the 
stroke  utilizes  the  expansive  power  of  the  steam.  (See  Fig. 
233,  Plate  I.) 

Compression  of  the  steam  follows  the  closing  of  the  ex- 
haust before  the  piston  has  completed  its  stroke.  This  is 
done  to  obtain  a  yielding  cushion  for  the  reciprocating  parts 
to  come  to  a  full  stop  without  shock  before  beginning  the 
return  stroke. 

Expansion  begins  at  the  point  of  cut-off  and  continues 
to  the  point  of  exhaust.  (See  Figs.  233  to  235  in  Plate 


ENGINE  DETAILS. 


309 


During  this  period  the  valve  travels  a  distance  equal  to  the 
outside  lap  plus  the  inside  lap. 

The  Allen-Richardson  Balance-valve — This  is  one  of 
the  most  popular  combination  slide-valves  and  is  used  on 
locomotives,  stationary  and  large  marine  engines.  Fig.  227 
clearly  shows  the  different'  parts  used  in  the  construction  of 
this  valve.  The  balance  is  effected  by  means  of  four  rect- 


1*1G     227. 

angular  packing-strips  5  fitted  into  grooves  on  the  top  of  the 
valve.  Semi-elliptic  springs  Z  are  used  to  hold  the  packing- 
strips  against  the  pressure-plate  P  when  there  is  no  steam  in 
the  chest,  but  when  steam  is  admitted  to  the  chest  it  forces 
the  strips  against  the  pressure-plate  and  sides  of  the  grooves, 
forming  a  steam-tight  joint  and  preventing  the  steam  from 
acting  on  that  part  of  the  top  of  the  valve  enclosed  by  the 
four  pncking-strips. 


3IO  DRAWING   AND    DESIGNING. 

Exercise  no. — Make  drawings  as  shown  in  Fig.  227,  and 
also  a  half  plan  of  the  top.  Scale  8"  =  I  foot. 

The  Allen  feature  of  this  valve  is  the  supplementary  port 
shown  at  A  just  above  the  exhaust-arch.  By  means  of  this 
additional  port  steam  is  admitted  to  the  same  steam-port  in 
the  cylinder  from  both  sides  of  the  valve  at  the  same  time, 
thereby  increasing  the  steam-supply  with  short  cut-offs.  The 
advantages  of  this  valve  over  the  plain  slide-valve  and  the 
objections  to  it  are  discussed  in  the  proceedings  of  the  fol- 
lowing societies:  A.  S.  M.  E.,  vol.  20,  May  1899;  The 
Western  Railway  Club,  March,  1897;  Am.  Railway  M.  M. 
Association,  1896;  and  in  the  "  Locomotive  up  to  Date  "  by 
Chas.  McShane. 

*  The  American  Balance  Slide-valve. —  The  American 
Balance  is  applied  to  any  type  of  slide-valve.  It  consists  of 
a  steam-tight  joint  being  formed  between  the  valve  and  the 
under  side  of  the  steam-chest  cover,  thus  excluding  live-steam 
pressure  from  a  given  area.  (See  Fig.  228.)  This  joint  is 
formed  by  a  bevelled  snap-ring  which,  when  in  place,  is 
slightly  expanded  over  a  cone.  The  cone  or  cones  are  either 
cast  with  the  valves  or  bolted  to  it,  as  circumstances  require. 

The  mechanical  construction  of  the  balance  is:  First,  the 
cone  or  two  cones,  where  necessity  requires,  are  either  bolted 
to  or  cast  with  the  valve.  The  snap- rings,  which  are  bevelled 
on  their  inner  side  to  a  corresponding  degree  with  that  of  the 
cone,  are  bored  smaller  in  diameter  than  their  required  work- 
ing diameter  so  that,  by  their  being  forced  down  on  the  cone 
by  the  placing  of  the  steam-chest  cover  in  position,  the  rings 

*  The  above  description  was  furnished  by  Mr.  J.  T.  Wilson,  Generai 
Manager  of  The  American  Balance  Slide-valve  Co. 


ENGINE   DETAILS. 

themselves  are  under  tension  and  are  thus  supported  by 
their  own  elasticity  when  not  under  steam.  The  steam  when 
admitted  to  the  steam-chest  exerts  a  pressure  on  the  entire 
circumference  of  the  ring,  which  has  a  tendency  to  close  it  or 
decrease  its  diameter,  and  owing  to  its  bevelled  face  and  the 
taper  of  the  cone  the  steam  also  acts  to  lift  it.  By  careful 


FIG.  228. 

consideration  of  the  operation  of  this  ring,  now  being  held  by 
the  steam-pressure  tightly  against  the  face  of  the  cone,  it  will 
at  once  be  seen  that  all  lateral  wear  is  avoided,  and  the  ring 
moves  as  a  part  of  the  cone  or  valve  itself.  It  will  also  be 
noted  that  the  ring  is  absolutely  compelled  to  assume  its  work- 
ing position  by  the  pressure  on  its  circumference.  When 
steam  is  shut  off  from  the  engine  and  the  engine  allowed  to 
drift,  as  in  locomotives,  the  valve  is  free  to  leave  its  seat  until 


312  DRAWING   AND   DESIGNING. 

the  cone  comes  in  contact  with  the  cover.  This  affords  per- 
fect and  ample  relief  of  the  air  which  the  piston  is  forcing 
from  one  end  of  the  cylinder,  and  also  a  direct  communication 
with  the  other  end  of  the  cylinder,  in  which  a  vacuum  is 
being  formed.  The  cylinders  are  therefore  perfectly  relieved 
by  allowing  the  valve  to  lift  \"  off  its  seat. 

The  bevelled  feature  in  the  ring  renders  the  ring  self-sup- 


FIG.  229. 

porting  when  not  under  steam,  and  supported  by  the  steam- 
pressure  when  under  steam,  automatic  adjustment  for  the 
wear,  positive  action  under  all  conditions,  and  self-maintaining 
the  steam-joint.  It  renders  it  possible  also  to  duplicate  the 
rings  of  respective  size"  in  repairs. 

Owing  to  the  absence  of  lateral  wear  on  the  cones  new 
rings  can  be  duplicated  at  any  future  time.  The  greatest  area 
of  balance  can  be  secured  by  this  design,  because  it  is  least 
affected  by  back  or  upward  pressure.  The  valve  in  order  to 


ENGINE   DETAILS. 


313 


leave  its  seat  must  first  expand  the  taper  ring  against  the 
chest-pressure  acting  on  its  circumference. 

The    features    enumerated    all    depend    upon    the    taper. 

Fig.  228  is  a  double-cone  balance-valve  used  on  locomo- 
tives. The  improved  T  ring,  the  invention  of  Mr.  J.  T.  Wilson, 
is  clearly  shown  in  the  figure. 

Fig.  229  is  a  single-cone  balance-valve  for  use  on  com- 
pound stationary  engines.  A  double-cone  valve  of  this  kind 
is  in  use  on  the  Japanese  cruiser  "  Chtose,"  the  rings  of  which 


FIG.  230. 

are  three  feet  ten  inches  in  diameter,  while  that  in  Fig.  229 
is  only  twenty  inches  diameter. 

Exercise  III — Make  drawings  of  Fig.  230  as  shown. 
Scale  6"  =  I  foot. 

The  Bilgram  Diagram. — Among  the  many  diagrams 
devised  to  determine  quickly  and  accurately  the  position  of 
the  valve  for  any  position  of  the  crank,  that  due  to  Mr. 
Hugo  Bilgram  is  one  of  the  simplest  and  best. 


DRAWING   AND   DESIGNING. 


FIG.  231. 


ENGINE  DETAILS.  31$ 

In  Plate  I  let  AB  represent  the  valve  circle,  equal  in  di- 
ameter to  the  travel  of  the  valve,  and  LI  the  centre-line  of 
the  crank  rotating  in  the  direction  of  the  arrow.  From  B 
lay  off  the  angle  EOB,  equal  to  the  angle  of  advance.  At  E 
describe  the  arc  bgk  with  a  radius  equal  to  the  inside  lap, 
and  also  the  arc  afd  with  a  radius  equal  to  the  outside  lap. 
Crank  positions  drawn  tangent  to  these  arcs  at  a,  b,  k,  and  d 
will  give  the  points  of  cut-off,  compression,  release,  and  ad- 
mission respectively,  as  indicated  in  the  figure. 

Let  us  follow  the  crank  through  one  revolution,  beginning 
with  the  dead-point  A.  In  this  position  de  is  equal  to  the 
outside  lead,  and  the  valve  has  moved  from  its  central  posi- 
tion a  distance  Ee  equal  to  the  lap  plus  the  lead.  These 
relations  are  clearly  shown  in  Fig.  231.  c  gives  the  distance 
which  the  valve  has  travelled  from  its  central  position,  and  at 
X  the  left-hand  steam-port  is  shown  open  to  steam  an  amount 
equal  to  the  lead  when  the  piston  is  at  the  beginning  of  its 
forward  stroke,  and  the  eccentric  is  connected  directly  to  the 
valve,  i.e.,  without  a  rocker. 

When  the  crank  reaches  the  position  L*  perpendicular  to 
OE  the  valve  will  have  travelled  from  its  central  position  a 
distance  equal  to  EO.  This  is  the  extreme  position  of  its 
forward  travel,  as  shown  in  Fig.  232.  The  maximum  open- 
ing of  the  port  X  to  steam  is  equal  to  Of,  and  the  overtravel 
to  mfy  the  actual  width  of  the  steam-port  being  =  Om. 

As  the  crank  leaves  D  the  valve  begins  to  return,  and 
when  the  crank  is  at  Z*  the  distance  of  the  valve  from  its 
central  position  is  equal  to  the  lap  ab.  Port  X  is  now  closed 
to  steam,  and  cut-off  is  accomplished  as  shown  in  Fig.  233. 

When  the    crank  is    at  U  the    right-hand  steam-port   is 


DRAWING   AND   DESIGNING. 


closed  to  exhaust,  and  compression  begins  as  shown  at  F, 
Fig.  234. 

When  the  crank  reaches  L]  the  valve  is  on  the  point  of 
opening  port  ^Y,  Fig.  235,  to  release  the  steam  which  was 
under  compression  during  the  time  the  crank  moved  from 
U  to  Z,1.  At  crank  position  L  we  find,  as  shown  in  Fig  236, 
that  the  valve  is  on  the  point  of  admitting  steam  to  port  F, 
and  at  B  the  backward  stroke  of  the  piston  begins,  the  valve 
having  opened  the  port  an  amount  equal  to  the  lead  de,  equal 
to  the  opening  shown  at  X  in  Fig.  231. 

At  crank  position  r  and  valve  position  Fig.  237  the 
valve  has  attained  its  maximum  travel  in  the  opposite  direction 
to  that  shown  in  Fig.  232.  At  l\  Fig.  238,  the  valve  cuts  off 
steam  from  port  F,  and  at  A  the  new  forward  stroke  begins. 

/3 


FIG.  239. 
Exercise  112. — (Fig.  239.) 

Given.  Required 

Travel =     5" '.  Outside  lap. 

Angle  of  advance. .  .  =  30°.  Inside  lap. 

Cut-off =  8o#  of  stroke.  Outside  lead. 

Compression =  90$  of  stroke.  Inside  lead. 

Width  of  steam-port  =     i  J''.  Maximum  port  opening. 

Overtravel. 


ENGINE   DETAILS.  317 

Draw  AB  and  CO  at  right  angles  to  one  another.  De- 
scribe the  valve-circle  arc  ACB  with  a  radius  equal  to  half 
the  travel  or  eccentricity  of  the  eccentric  —  2\"  to  the  scale 
of  twice  full  size.  From  B  lay  off  the  angle  EOB  equal  to 
the  angle  of  advance  =  30°.  Let  AB  represent  the  stroke, 
and  from  A  lay  off  Al  =  80$  of  a  stroke  of  24",  and  erect  a 
perpendicular  to  cut  the  valve  circle  in  /'.  Draw  OL3  through 
r  ;  this  is  the  crank  position  at  the  point  of  cut-off.  Through 
E  perpendicular  to  OL*  draw  Ea.  With  centre  E  and  radius 
Ea  describe  the  lap  circle  afd.  From  A  lay  off  A2  =  90$  of 
the  stroke,  and  erect  a  perpendicular  to  cut  the  valve  circle 
at  b.  Through  b  draw  OL*,  which  is  the  crank  position  at  the 
point  of  compression.  With  E  as  centre  and  Eb  as  radius 
describe  the  inside  lap  circle.  Draw  OU  tangent  to  bgk  at 
point  k. 

At  O  with  a  radius  =  the  port  opening  describe  the  arc 
h.  Then  Ea  is  the  required  lap,  Eb  the  inside  lap,  de  the 
lead,  ke  the  inside  lead,  (9/the  maximum  port-opening,  and 
hf  the  overtravel. 

Exercise  113. — (Fig.  240.) 

Given.  Required. 

Cut-off =  80$  of  stroke.       Travel  of  the  valve. 

Lap —     \" .  Angle  of  advance. 

Lead =     J". 

Draw  to  a  scale  equal  to  twice  full  size  AB  and  CO  at  right 
angles.  Draw  OL*t  the  position  of  crank  at  cut-off.  Draw 
line  I  2  parallel  to  AB  at  a  distance  above  it  equal  to  the 
lead  ed.  Draw  line  3  4  parallel  to  AB  at  a  distance  equal  to 
the  lap  plus  the  lead  above  it.  With  a  radius  equal  to  the 


DRAWING   AND   DESIGNING. 

given  lap  find  by  trial  a  centre  on  the  line  3  4,  and  draw  the 
lap  circle  afd  tangent  to  OD,  and  line  I  2  at  the  points  a 
and  d. 


Then  through  E  with  centre  O  describe  the  valve  circle 
ACB. 

AB  is  the  travel  of  the  valve,  and  EOB  the  angle  of  ad- 
vance. 

C 


FIG.  241. 
Exercise  114 — (Fig.  241.) 

Given.  Required. 

Cut-off =  8o#  of  the  stroke.  Travel  of  the  valve, 

Admission =  90$  of  the  stroke.  Lead. 

Maximum  port-opening  =  Of  (Fig.  240).    Angle  of  Advance. 

Lap. 


ENGINE   DETAILS. 


319 


Draw  AB  and  CO  at  right  angles.  Draw  OL,  the  posi- 
tion of  the  crank  at  the  point  of  admission.  Draw  OL't  the 
crank  position  at  cut-off,  and  arc /with  a  radius  equal  to  the 
given  maximum  port-opening.  Bisect  the  angle  LOL*  with 
the  line  OE.  The  centre  of  the  lap-circle  will  be  on  this 
line.  Draw  /;;/  perpendicular  to  OL*,  and  make  fn  =  fm. 
Through  f  draw  fa  parallel  to  nm,  and  aE  parallel  to  mf. 
E  is  the  centre  of  lap  circle.  Through  E  describe  the  valve 
circle  ACB,  and  draw  the  line  Ee  at  right  angles  to  AB. 

Then  AB  is  the  travel  of  the  valve,  Ea  the  lap,  BOE 
the  angle  of  advance,  and  de  the  lead. 


FIG.  242. 
Exercise  115 — (Fig.  242.) 

Given.  Required. 

Cut-off =  80^  of  the  stroke.   Angle  of  advance. 

Lead =    I".  Lap. 

Maximum  port-opening  =  Of  (Fig.  240).    Travel  of  valve. 

Draw  AB  and  CO  at  right  angles.  Locate  the  crank 
position  OL\  Draw  the  lead-line  I  2  at  a  distance  de  from 
AB  and  parallel  to  it.  With  centre  O  describe  arc  3  4  with 
a  radius  equal  to  the  maximum  port-opening.  Find  by  trial 
the  centre  E  of  a  circle  that  can  be  Jrawn  tangent  to  OL*,  arc 
3  4,  and  line  I  2.  Through  this  centre  draw  OE. 


320  DRAWING  AND   DESIGNING. 

Then  BOE  is  the  angle  of  advance,  Ea  the  lap,  and  twice 
OE  is  equal  to  the  travel  of  the  valve. 

The  Zeuner  Valve  Diagram — In  Plate  II  let  AB  repre- 
sent the  stroke  of  the  piston,  the  circle  ACBD  the  path  of 
the  crank-pin,  and  L  the  centre-line  of  the  crank. 

From  C  lay  off  OE  equal  to  the  angle  of  advance,  and  on 
OE  as  a  diameter  describe  the  valve  circle  equal  to  half  the 
travel  of  the  valve  or  eccentricity  of  the  eccentric  when  no 
rocker  is  used.  From  centre  O  draw  the  arcs  abc  and  gfh 
equal  to  the  outside  and  inside  laps  respectively. 

At  the  beginning  of  the  forward  stroke  the  true  position 
of  the  crank  would  coincide  with  AO,  and  the  centre-line  of 
the  eccentric  with  OE. 

Now  since  the  position  of  the  point  E  is  fixed  for  a  given 
eccentricity  and  angle  of  advance,  the  point  E  will  always  be 
found  on  the  circumference  of  the  circle  having  OE  as  a  diam- 
eter; and  if  the  valve  circle  together  with  the  crank  be  rotated 
around  the  centre  O  in  a  direction  opposite  to  the  arrow,  its 
intersection  with  the  line  OB  from  O  will  be  the  distance 
which  the  valve  has  travelled  from  its  central  position  after 
the  crank  has  moved  through  any  given  angle. 

But  instead  of  rotating  the  crank  and  valve  circle  let  them 
remain  fixed  and  rotate  the  line  OB  as  an  imaginary  crank  in 
the  direction  of  the  arrow,  and  the  same  results  will  be  ob- 
tained in  a  much  simpler  way. 

Draw  OL,  the  imaginary  crank,  through  the  point  where 
the  lap  arc  abc  intersects  the  valve  circle  at  the  point  c.  The 
position  of  the  valve  will  then  be  at  the  point  of  admission, 
because  the  valve  will  have  travelle4  from  its  central  position 
a  distance  equal  to  Oc,  equal  to  the  lap. 


ENGINE  DETAILS. 


321 


322  ERA  WING   AND   DESIGNING. 

This  is  clearly  shown  in  Fig  243.  The  valve  is  travelling 
In  a  direction  opposite  to  the  imaginary  crank,  and  the  steam 
edge  /  of  the  valve  is  on  the  point  of  admitting  steam  to  the 
port  X  just  before  the  beginning  of  the  forward  stroke. 
When  the  imaginary  crank  reaches  the  position  OB  the  valve 
will  have  travelled  a  distance  equal  to  Oc  from  its  central 
position  and,  OB  being  a  dead-centre,  the  valve  will  have 
opened  the  port  X  to  steam  an  amount  equal  to  the  lead,  and 
the  port  Y  to  exhaust  an  amount  equal  \.Q  pq,  Fig.  244. 

When  the  crank  has  reached  the  position  OE  the  valve 
will  then  have  attained  the  extreme  position  of  its  travel. 
The  shaded  part  bk  shows  the  full  opening  of  the  steam-port, 
and  ke  the  amount  of  overtravel,  and  at  the  same  time  the 
port  Fis  fully  open  to  exhaust,  as  shown  by  the  shaded  por- 
tion fj,  and  JF  is  the  exhaust  overtravel  (Fig.  245). 

The  valve  now  returns  and  at  R  begins  to  close  port  X, 
until  when  the  crank  arrives  at  Z8  the  port  is  fully  closed  and 
cut-off  takes  place,  as  shown  in  Fig.  246. 

When  the  crank  is  in  the  position  L4  at  right  angles  to  OE 
the  valve  is  in  its  middle  position,  as  shown  in  Fig.  247. 

At  the  crank  position  U  the  valve  has  travelled  a  distance 
Og  from  its  central  position,  and  the  port  X  is  about  to  open 
to  exhaust,  as  shown  in  Fig.  248.  The  port  continues  to 
open,  until  at  the  position  L1  the  port  is  fully  open  and  con- 
tinues so  until  the  crank  reaches  the  position  L\  when  it  begins 
to  close,  and  is  fully  closed  when  the  crank  reaches  L?.  Now 
compression  begins  and  continues  through  the  angle  L?OL. 
At  L  the  valve  has  returned  to  the  point  of  admission  a  little 
before  the  beginning  of  the  new  forward  stroke. 

At  crank  position  Z8  it  will  be  seen  from  Fig.  250  that  the 


ENGINE  DETAILS. 


323 


port  Fis  fully  open  to  steam,  the  port  X  fully  open  to  exhaust, 
and  that  the  valve  has  reached  the  extreme  position  of  its 
travel  for  the  backward  stroke — just  the  opposite  of  the  posi- 
tion shown  in  Fig.  245. 

C 


$0%  Stroke 

-90%Stroke r 

FIG.  252. 

Exercise  116 — (Fig.  252).  Assume  the  same  conditions 
as  in  Ex.  1 12  for  the  Bilgram  diagram.  Draw  AB  and  CO  at 
right  angles.  Make  AB  to  any  convenient  scale  equal  to  the 
stroke  of  the  piston,  and  let  ACB  represent  the  path  of  the 
crank-pin.  From  C  lay  off  angle  OE  equal  to  the  angle  of 
advance  =  30°,  with  a  scale  equal  to  twice  full  size.  On  Ok 
as  a  diameter,  equal  to  half  the  travel  of  the  valve,  or  2 J",  de- 
scribe the  valve  circle  Oakc.  From  B  lay  off  Bl  equal  to  8o# 
of  the  stroke,  and  erect  a  perpendicular  to  cut  the  crank-pin 
arc  in  V '.  Draw  OL*,  the  position  of  the  crank  at  cut-off. 
Through  the  point  a,  where  OL9  cuts  the  valve  circle,  with  O 
as  centre  describe  the  arc  abc.  From  B  lay  off  B2  equal  to  90$ 
of  the  stroke,  and  erect  a  perpendicular  to  L*.  Draw  OL',  and 
through  the  point  g,  where  OL*  intersects  the  valve  circle, 
with  .  O  as  centre  describe  the  arc  gfh.  From  b  lay  off  bk 
equal  to  the  width  of  the  steam-port,  and  with  centre  O  and 
radius  Ok  describe  the  arc  3^4. 


324 


DRAWING   AND   DESIGNING. 


Then  Oa  is  the  required  lap,  Og  the  inside  lap,  de  the 
lead,  5^  the  inside  or  exhaust  lead,  OE  the  maximum  port- 
opening,  and  KE  the  overtravel. 

C 


O 

FIG.  253. 

Exercise  117. — (Fig.  253.)  Assume  the  same  conditions 
as  given  in  Ex.  113. 

Draw  AB  and  CO  at  right  angles.  Draw  OL3,  the  crank 
position  at  cut-off.  From  O  describe  arc  abc  with  a  radius 
equal  to  the  lap,  scale  as  before.  Lay  off  de  equal  to  the 
lead.  Bisect  Oa  and  Oc,  and  the  point  /where  the  bisectors 
intersect  will  be  the  centre  of  the  valve  circle  which  may  now 
be  drawn  through  the  points  aOe. 

Then  OE  is  equal  to  half  the  travel  of  the  valve,  and  COE 
is  the  angle  of  advance. 

Exercise  118. — (Fig-  254.) 

Given. 

Point  of  cut-off. .  .   =  80$  of  stroke. 
Point  of  admission  =  90$  of  stroke. 

Lead =  J". 

Draw  AB  and  CO  at  right  angles, 
tions  OL  and  OL\  Bisect  the  angle  LOL*  with  the  line  OE. 
On  OE  assume  any  point  as  g,  and  draw  gf  perpendicular  to 
OB,  and  gh  perpendicular  to  OL.  With  center  O  and  radius 
Oh  describe  the  arc  he. 


Required. 

Travel  of  valve. 
Lap. 

Angle  of  advance. 
Draw  the  crank  posi- 


ENGINE  DETAILS.  325 

Now  the  angles  gOB  and  gOL  are  constant  for  a  given 
admission  and  cut-off;  therefore  the  lead  will  vary  directly  as 
the  eccentricity. 


Let  Og  be  an  assumed  eccentricity,  then  ef  will  be  its  cor- 
responding lead,  and  the  given  lead  is  to  the  assumed  lead 
</"as  the  required  eccentricity  is  to  the  assumed  eccentricity 

os. 

Lay  off  Ol  equal  to  the  given  lead,  and  O2  equal  to  ef. 
Draw  2g,  and  IE  parallel  to  2g. 

With  a  radius  equal  to  Oe  minus  the  given  lead  and  centre 
O  describe  the  arc  abc.  On  OE  as  a  diameter  describe  the 
valve  circle  Oaec. 

Then  COE  is  the  required  angle  of  advance,  OE  the  ec- 
centricity or  half  the  travel  of  the  valve,  and  Oa  the  lap. 

Exercise  119. — (Fig.  255.)  Assume  the  conditions  as  in 
Ex.  115. 

Draw  AB  and  CE  at  right  angles  to  each  other.  Draw  OL\ 
the  crank  position  at  cut-off,  Oa,  the  given  lead,  and  Ob,  the 
given  maximum  port-owning.  At  b  erect  the  perpendicular 
bg.  Through  a  draw  ad  at  right  angles  to  OL\  Bisect  the  angle 
dee  with  the  line  Oc,  and  produce  it  to  intersect  y%-  at  g.  Join 


326 


DRAWING   AND    DESIGNING. 


ag,  and  draw  cf  parallel  to  Ob.  With  c  as  centre  and  cf  as 
radius  describe  arc//£,  cutting  ag  in  k.  Join  ck,  and  draw  a  O 
parallel  to  kct  cutting  O^g  in  the  point  <?,.  Draw  O^e  parallel 
to  O,A. 

Then  Ock  is  the  required   angle  of  advance,  O^a  half  the 
required  travel  of  the  valve,  and  Ote  the  lap. 


Engine  Frame  or  Bed-plate. — Frames  for  horizontal 
engines  are  usually  made  of  cast  iron.  This  is  the  most  suit- 
able material  owing  to  the  complicated  sections  found  in  most 
frames,  and  also  because  it  gives  the  necessary  rigidity. 

Figs.  256  to  258  show  an  engine  frame  of  the  "  Tangye  " 
type.  It  is  that  used  by  the  Buckeye  Engine  Co.  of  Salem, 
Mass. 

Exercise  120. — Make  drawings  as  shown  in  Figs.  256  to 
258.  Scale  \%'  —  I  foot. 


ENGINE  DETAILS. 


327 


328  DRAWING   AND   DESIGNING. 

Cylinder.  —  Steam-engine  cylinders  are  almost  always  made 
of  a  tough,  close-grained  cast  iron  as  hard  as  can  be  safely 
worked. 

Diameter  of  Cylinder,  D. 

Let  P  =  the  mean  effective  pressure  of  steam  in  pounds  per 
square  inch  =  M.  E.  P.  ; 

L  =  length  of  stroke  in  feet  ; 

A  =.  area  of  piston  in  square  inches; 

N  =  number  of  strokes  per  minute. 

PL  A  N 

Then  -  -  =  I.H.P.   or    indicated  horse-power,   and 

33000 

I.H.P.  X  33000  A 


PLN  j 

The  mean  effective  pressure  P  may  be  found  from    the 
following  formula: 

Let/  =  the  absolute  initial  pressure  of  steam,  i.e.,  the 
gauge-pressure  -j-  15  Ibs.  ;  —  7$  for  loss  between 
boiler  and  cylinder. 

r  =  ratio  of  expansion  =  length  of  stroke  in  inches  -=- 
distance  travelled  by  piston  in  inches  before 
steam  is  cut  off. 

I  _j_  hyp.  log.  r 
Then  P=  -  --  back-pressure. 

Thickness  of  Cylinder,  t. 

Let  P,  =  boiler-pressure    of    steam    per    square    inch    in 

pounds; 
D  =  diameter  of  cylinder  in  inches. 

"  Whitham  "  recommends  the  following  formula  for  hor- 
izontal or  vertical  cylinders  of  large  or  small  diameter  where 


ENGINE  DETAILS.  329 

provision  is  made  for  reboring  and  sufficient  strength  and  rig- 
idity are  secured  : 

/  =  0.03  VP^D. 

Length  of  Cylinder.  —  The  length  of  cylinder  between 
heads  =  Stroke  -f-  thickness  of  piston  +  the  sum  of  the  piston 
clearance  at  both  ends. 

Cylinder  Head.  —  The  cylinder  head  or  cover  next  to  the 
crank  is  sometimes  cast  on  the  cylinder.  ' 

The  thickness  of  the  cylinder  head  recommended  by  Prof. 
Seaton  is  • 

P^D  -f  500 

2000 

The  thickness  at  the  flange  where  the  head  is  bolted  to  the 
cylinder  should  be  -J-  greater  than  this. 

Cylinder-head  Bolts.  —  The  diameter  of  cylinder-head 
studs  in  locomotives  is  usually  J",  and  their  pitch  about  4 
times  their  diameter. 

For  stationary  and  marine  practice  "  Ripper"  gives 


4  4 

where  n  =  number  of  studs; 
d=  diameter  of  studs; 
D  =  diameter  of  cylinder; 
/  =  maximum  pressure  of  steam  ; 
/=  4000  to  5000. 

Steam-ports.  —  The  steam-ports  which  conduct  the  steam 
from  the  valve-chest  to  the  cylinder  should  be  as  short  and 
direct  as  possible,  but  large  enough  to  prevent  wire-drawing 
and  of  easy  curvature. 


33°  DRAWING  AND   DESIGNING. 

The  length  of  ports  in  locomotives  is  usually  i"  less 
than  the  diameter  of  the  cylinder. 

In  other  types  the  length  is  generally  made  o.8Z>. 

The  area  of  the  steam-port  is  given  by  many  authorities 
as  follows : 

AV 
a  — , 

v 

where  A  =  area  of  the  piston  in  square  inches ; 

v  —  velocity  of  steam  through  the  port  =  6000  feet  per 

minute ; 
V '=  velocity  of  piston  in  feet  per  minute  (from  1000 

to  1200); 

a  =  area  of  steam-port. 

Figs.  259  to  262  show  the  working  drawings  of  a  horizon- 
tal steam-engine  cylinder  made  by  the  Buckeye  Engine  Co. 
Fig.  259  shows  a  longitudinal  section  through  the  centre  of 
the  cylinder,  Fig.  260  a  cross-section  through  the  exhaust- 
passage,  Fig.  261  a  back-end  view  showing  the  opening  for 
a  valve-rod,  and  Fig.  262  a  plan. 

Figs.  263  and  264  are  the  heads  and  covers  suitable  for 
this  cylinder.  When  in  position  on  the  engine-frame  the  end 
of  the  cylinder,  shown  in  Fig.  261,  is  bolted  to  the  end  of 
the  frame  shown  in  Fig.  261. 

Exercise  121. — Make  drawings  of  steam-cylinder  as  shown 
in  Figs.  259  to  262.  (Scale  i^"  =  i  foot.} 

Exercise  122 — Make  the  design  of  a  cylinder  similar  to 
that  shown  in  Figs.  259  to  262  to  develop  100  I.H.P.  Stroke 
30" ;  steam-pressure  90  Ibs.  per  square  inch ;  cut-off  at  50$ 
of  the  stroke.  Number  of  strokes  per  minute  220. 


ENGINE   DETAILS. 


331 


332  DRAWING   AND   DESIGNING. 

Exercise  123.  —Make  drawings  of  the  cylinder  heads  shown 
in  Figs.  263  and  264.  (Scale  i\"  =  i  foot.) 

Pistons. — A  piston  is  that  part  of  an  engine  or  pump 
which  slides  to  and  fro  inside  a  hollow  cylinder  either  driven 
by  fluid  pressure  or  acting  against  fluid  pressure  they  are 
usually  of  circular  section  and  are  made  of  brass,  wrought  iron, 
cast  iron,  or  steel. 

A  piston  with  valves  which  permit  the  fluid  to  pass  from 
one  side  to  the  other  is  called  a  bucket  and  is  used  in  pump 
cylinders. 

A  single-acting  piston,  guided  by  the  stuffing-box  instead 
of  the  cylinder,  is  called  a  plunger  and  is  also  used  in  pumps. 

Steam-pistons. —  A  steam-piston  should  be  designed  so 
as  to  prevent  the  steam  from  passing  from  one  side  of  the 
piston  to  the  other. 

The  spring  packing-rings  should  not  press  against  the  cyl- 
inder more  than  is  necessary  for  steam-tightness. 

A  piston  should  be  no  heavier  than  is  necessary  for 
strength. 

The  weight  of  the  piston  should  be  distributed  so  as  to 
prevent  the  excessive  internal  wear  of  the  cylinder. 

The  piston  must  be  firmly  connected  to  the  piston-rod. 

Many  different  designs  have  been  adopted  to  secure  the 
above  requirements. 

Fig.  265  is  a  plain  box  piston,  used  by  the  Southwark 
Foundry -&  Machine  Company.  It  is  cast  in  one  piece;  the 
core  being  removed  by  three  holes,  shown  in  the  front,  which 
are  afterwards  plugged  up.  The  two  small  holes  are  for  eye- 
bolts  which  are  used  to  remove  the  piston  from  the  cylinder 
when  necessary.  The  packing  consists  of  two  cast-iron  spring 


ENGINE   DETAILS. 


333 


rings  cut  as  shown  in  detail  in  the  figure.  The  rod  is  forced 
into  place  by  pressure  and  the  ends  riveted  over. 

Exercise  124.— Make  drawings  as  shown  in  Fig.  265. 
(Scale  6"  =  /  foot.) 

Fig.  266.  This  is  another  style  of  box  pattern,  used  by 
the  Ball  Engine  Company.  The  style  of  packing  and  the 
method  of  securing  the  piston-rod  are  plainly  shown  in  the 
figure. 


FIG.  265. 


FIG.  266. 


Exercise  125. — Make  drawings  as  shown  in  Fig.  266,  and 
in  addition  make  a  half  end  section  through  the  centre  of  the 
piston.  (Scale  6''  =  I  foot.) 

Fig.  267  shows  a  common  built-up  piston  used  largely  in 
locomotives.  It  consists  of  a  spider,  S,  a  T  ring,  a  follower,  F9 
and  two  cast-iron  spring-rings.  The  rod  is  forced  into  place 
and  held  by  nut  over  which  the  end  of  the  rod  is  riveted. 

Exercise  126. — Make  drawings  of  a  built-up  piston  like 
Fig.  267  for  an  engine  whose  cylinder  is  18''  X  24''. 
Take  dimensions  from  Table  36.  (Scale  6"  =  I  foot.) 

Fig.  268,  a  cast-iron  box  piston  used  in  the  cylinder  of  the 
Empire  State  Express  locomotive.  Its  construction  is  plainly 
shown  in  the  figure. 


334 


DRAWING   AND   DESIGNING. 


Exercise  127. — Make  drawings  of  the  piston  shown  in  Fig. 
268.     (Scale  6"  =  /  foot.) 

Fig.  269  is  a  cast- steel  box  pattern  cast  in  two  parts  and 


FIG.  267. 
TABLE  36. 


15 
16 
18 
19 

20 
22 


3f 

4 
4 

4 

J| 


if 
2 

2} 

2  8 

2§ 

3 


if 

if 

It 


ENGINE  DETAILS. 


335 


FK;    2.x;. 


336 


DRAWING   AND    DESIGNING. 


L_ 


ENGINE  DETAILS.  337 

held  together  by  rivets.  This  piston  is  made  by  the  Baldwin 
Locomotive  Works  for  the  "  Vauclain  "  compound  locomo- 
tive. 

Exercise  128. — Make  drawings  as  shown  in  Fig.  269. 
(Scale  4."  =  i  foot.) 

Fig.  270  shows  the  cast-iron  pistons  used  in  tandem 
stationary  engines  built  by  Mclntosh  &  Seymour. 

The  packing  is  composed  of  cast-iron  spring-rings  cut  and 
kept  in  place  by  the  method  shown  in  detail  in  the  figure. 
The  arrangement  for  securing  the  rod  is  shown  in  detail  in 
Fig.  68,  page  103. 

Exercise  129. — Make  drawings  as  shown  in  Fig.  270. 
(Scale  3"  =  I  foot.) 

Fig.  271  is  a  built-up  piston  for  the  Tangye  stationary 
engines  made  by  the  Buckeye  Engine  Co.  It  consists  of  a 
spider,  follower,  and  adjusting-screws.  There  are  no  springs; 
the  screws  act  on  an  uncut  junk-ring,  so  can  only  be  used  for 
centring,  not  for  packing.  The  packing-rings  are  turned 
larger  than  the  bore  of  the  cylinder  so  as  to  pack  by  their  own 
elasticity.  They  may  or  may  not  be  turned  eccentric,  that  is, 
thin  where  cut,  and  full  thickness  opposite  the  cut. 

If  made  eccentric,  it  is  for  the  reason  that  they  will  be 
more  nearly  round  when  sprung  into  the  cylinder. 

Exercise  130. —  Make  drawings  as  shown  in  Fig.  271. 
(Scale  6"  =  I  foot.) 

Fig.  272  shows  a  water-piston  suitable  for  cylinders  under 

9"  diameter. 

The  piston-rod  is  fitted  to  the  head  with  a  shoulder  to 
drive  the  piston,  and  the  rod  is  secured  in  place  by  a  nut. 
The  follower  is  also  held  by  a  nut  and  lock-nut.  By  this 


338 


DRAWING   AND    DESIGNING. 


ENGINE  DETAILS.  339 

means  the  follower  and  packing  may  be  adjusted  or  renewed 
at  will.  The  packing  is  made  of  layers  of  cotton  cloth  and 
sheet  rubber. 

Exercise  131 — Make  drawings  of  water-piston  as  shown 
fn  Fig.  272.  (Scale  full  size.) 

Connecting-rods. —In  steam  and  other  engines  the  con- 
necting-rod connects  the  rotating  crank  with  the  reciprocat- 
ing cross-head. 

There  are  many  styles  of  connecting-rods,  and  various 
methods  are  employed  for  taking  up  the  wear  of  the  brasses. 
Figs.  273  to  276  show  good  examples  of  rods  used  in  station- 
ary, locomotive,  and  marine  engines  of  the  most  modern 
types. 

Fig-  273  is  tne  r°d  used  by  the  Buckeye  Engine  Co.  for 
their  "  Tangye  "  type  of  engine.  The  crank  end  is  solid,  the 
brasses  are  lined  with  babbitt,  and  adjustment  for  wear  is  had 
by  means  of  a  tapered  steel  block  and  screws.  The  cross- 
head  end  is  called  a  strap  end.  The  strap  is  firmly  bound  to 
the  end  of  the  rod  with  a  cotter-key  and  gib,  which  also  con- 
trols the  adjustment  for  wear. 

Fig.  274  has  strap  ends  front  and  back.  Keys  are  in- 
serted between  the  straps  and  the  rod  to  prevent  the  shear  of 
the  strap-bolts.  The  construction  of  this  rod  and  the  method 
employed  to  take  up  the  wear  are  plainly  shown  in  the  figure. 
The  Erie  City  Iron  Works  use  this  rod  on  their  stationary 
engines. 

Exercise  132 — Make  the  drawings  as  shown  in  Fig.  273. 
(Scale  6"  =  i  foot.) 

Exercise  133 — Make  the  drawings  as  shown  in  Fig.  274, 


340 


DRAWING   AND   DESIGNING. 


ENGINE  DETAILS. 


341 


342  DRAWING   AND    DESIGNING. 

except  that  half  of  the  plan  shall  be  a  section  through  XX. 
(Scale  6"  =  i  fact.) 

Fig.  27$  is  the  connecting-rod  used  by  the  Pennsylvania 
Railroad  Company  on  their  fast  passenger-locomotives.  The 
crank  end  of  this  rod  is  an  improved  design  invented  by  Mr. 
A.  S.  Vogt,  mechanical  engineer  of  the  company.  He  ex- 
plains the  improvements  as  follows: 

As  before,  the  back  end  of  the  rod  is  forked,  but  the 
method  of  closing  the  open  end  of  the  fork  is  entirely  differ- 
ent, and  the  key  for  closing  the  main  brasses  has  been  moved 
from  the  forward  side  of  the  brass  to  the  rear,  which  has  an- 
other good  effect,  viz.,  as  the  brasses  in  both  front  end  and 
back  end  of  the  rod  wear  and  are  closed  up  to  meet  that 
wear,  the  actual  length  of  the  rod  changes  but  very  little,  for 
the  reason  that  the  keying  of  both  ends  is  in  the  same  direc- 
tion, whereas  in  the  old  form  of  the  rod  the  keying  was  in 
opposite  directions,  and  as  a  matter  of  course  the  distance 
from  centre  of  crank-pin  to  centre  of  crosshead-pin  increased 
gradually.  The  open  end  of  the  fork  in  this  rod  is  closed, 
first,  by  a  U-shaped  block,  the  detail  of  which  is  marked  A 
on  Fig.  275;  next,  by  the  key  which  is  marked  B\  and  last 
of  all  by  a  combined  key  and  bolt  marked  C;  this  bolt  clamp- 
ing the  two  members  of  the  fork  against  the  block  A  and 
forming  an  enclosed  surface  for  the  key  to  drive  against.  To 
prevent  the  slacking  up  of  the  nut  C,  a  keeper-block  is  pro- 
vided at  the  bottom  of  the  lower  member  of  the  fork.  This  is 
made  with  a  recess  into  which  the  nut  fits  and  a  set-screw  for 
locking  the  nut.  The  same  keeper-block  extends  forward  to 
the  key  B,  which  is  also  blocked  by  a  set-screw  in  the  block. 
It  is  quite  evident  that  there  is  much  less  chance  of  shearing 


ENGINE  DETAILS. 


343 


344  DRAWING   AND    DESIGNING. 

or  offsetting  of  the  bolt  and  the  key  in  this  than  there  was  of 
the  bolt  in  the  former  design  ;  but  even  if  it  should  take  place, 
which  is  not  very  likely,  the  whole  thing  can  readily  be  dis- 
connected by,  first,  driving  the  key  B  out,  unscrewing  the 
nut  on  the  bolt  and  moving  the  whole  bolt  slightly  forward, 
when  it  can  be  lifted  out  at  the  top. 

Exercise  134. — Make  drawings  as  shown  in  Fig.  275. 
(Scale  6"  =  i  foot.} 

This  form  of  rod  is  called  a  marine  connecting-rod  be- 
cause it  is  often  used  on  marine  engines,  but  it  is  also  largely 
used  on  stationary  engines  and  is  occasionally  seen  on  loco- 
motives. 

The  crank-pin  end  or  stub  is  usually  forged  solidly  on 
the  rod,  and  all  but  the  sides  is  finished  by  turning  in  the  lathe. 
The  sides  are  then  planed  and  the  bolt-holes  drilled.  The 
hole  to  receive  the  brasses  may  now  be  bored  unless  the  top 
and  bottom  of  the  brasses  are  to  be  thicker  than  the  sides,  in 
which  event  the  hole  will  not  be  completed  until  after  the  cap 
or  top  end  of  the  stub  has  been  slotted  off  and  bolted  on 
again. 

It  will  be  seen  that  the  bolts  are  turned  down  to  a  diam- 
eter equal  to  the  diameter  at  the  bottom  of  the  threads.  This 
does  not  weaken  the  bolt,  but  makes  it  more  elastic. 

The  cross-head  end  of  this  rod  is  made  forked  to  suit  the 
cross-head,  but  it  will  be  seen  that  each  half  of  the  forked  end 
is  constructed  the  same  as  in  the  large  end. 

A  detail  drawing  of  the  bolt  and  its  locking  arrangement 
is  given  in  Fig.  65,  page  96. 

Exercise  135. — Make  drawings  as  shown  in  Fig.  276. 
(Scale  2"  =  i  foot.} 


ENGINE   DETAILS.  345 

Thrust  of  Connecting-rod.  —  Assuming  that  a  connect- 
ing-rod is  equal  to  a  pillar  rounded  or  jointed  at  both  ends, 
let  D  =  diameter  of  piston  in  inches; 

L  —  length  of  stroke  in  inches; 
/  =  length  of  connecting-rod  in  inches; 

P=  maximum  steam-pressure  per  square  inch; 

T  =  thrust  of  connecting-rod. 

When  the  crank-pin  is  on  a  dead-centre  and  the  connect- 
ing-rod is  in  line  with  the  piston-rod,  then 


the  total  load  on  the  piston.  But  as  the  crank  rotates  the 
connecting  rod  becomes  inclined  to  the  centre  line  of  motion, 
and  T  increases  as  the  angle  of  the  connecting-rod  increases 
.until  a  maximum  is  reached  at  half-stroke,  provided  the  steam 
is  not  cut  off  before. 

The  value  of  T  may  be  found  for  any  position  of  the 
crank  as  follows: 

Let  AB,  Fig.  277,  be  the  connecting-rod,  and  BC  the 
crank.  The  forces  acting  at  A  are  Wy  the  maximum  pressure 
on  the  piston,  and  R,  the  reaction  of  the  guide  on  the  cross- 
head,  and  Tj  the  thrust  along  the  connecting-rod. 

From  the  triangle  of  forces 

T  _AB 
W~AC 
and 


AC'      VAff-Ac*       J,,    L'        v^r-r 


DRAWING   AND   DESIGNING. 

Diameter  of  Connecting-rod,  Circular  Section.  —  Thurs- 


ton  gives 


d  =  a</Dl,  VP+C=  diameter  at  middle, 
0.15  for  fast  engines, 


where  a  •=. 

0.08  for  moderate  speed ; 

J"  for  fast  engines, 
£ "  for  moderate  speed  ; 
/,  —  length  of  connecting-rod  in  feet. 
Seatons,  Marks,  and  Whitham  give 


d=  0. 


FIG.  277. 

For  the  diameter  at  the  crank-pin  end  Whitham  gives 
1. 08  times  the  diameter  at  the  cross  head  end.  The  rod  is 
larger  at  the  middle  and  tapers  about  $"  to  the  foot. 

Sennett  gives  diameter  at  middle  =  —  VP; 

"  necks     =~ 
60 


ENGINE   DETAILS. 


347 


Locomotive  Connecting-rods. — The  sizes  of  rectangular 
rods  of  uniformly  tapered  section  are  in  practice  as  follows: 

Depth  of  Main  Rod. — On  engines  with  cylinders  14"  di- 
ameter or  less  the  depth  of  the  rod  at  the  crank  end  is  made 
•J''  less  than  the  depth  of  the  stub;  over  14"  diameter,  -J" 
less. 

Depth  of  main  rod  at  cross- he  ad  end  =  </,. 


Cyl. 

diam. 

14" 

15" 

16" 

17" 

18" 

19" 

20" 

</, 

2f" 

2f" 

3" 

3" 

3" 

3" 

3i" 

Thickness  of  main  rod  =  /,. 

Cyl. 

diam. 

14" 

15" 

16" 

17" 

18" 

19" 

20" 

/, 

if" 

If" 

if 

if" 

2" 

2" 

2" 

Depth  of  Side-rods. — The  depth  of  the  side-rod  is  made 
about  •§"  narrower  than  that  of  the  stub  end,  and  of  uniform 
depth  throughout. 

Thickness  of  side -rods  =  /,. 


Cyl. 
diam. 

14" 

15" 

16" 

17" 

18" 

19" 

20" 

/a 

if" 

if" 

if" 

if" 

if" 

if" 

If" 

Pivot  or  Step  Bearing. — In  this  form  of  bearing  the 
pressure  is  applied  in  the  direction  of  the  axis,  and  the  load 
is  carried  entirely  upon  the  end  of  the  shaft.  In  lubricating 
a  bearing  of  this  type  the  oil  should  always  be  introduced  be- 
tween the  bearing  surfaces  from  the  under  side  and  in  the 
centre  of  the  bearing,  that  the  oil,  under  the  influence  of  the 


34-8  DRAWING   AND   DESIGNING. 

centrifugal  force,  will  be  distributed  over  the  entire  rubbing 
surface.  The  best  results  are  obtained  from  running  the 
bearing  in  a  bath  of  oil,  as  shown  in  Fig.  278,  where  the  oil- 
basin  surrounds  the  journal-box,  which  can  be  kept  submerged 
in  oil,  thus  insuring  constant  and  efficient  lubrication.  In 
Fig.  278  the  oil  passes  from  the  oil-basin  OB  to  the  journal- 
box  through  the  hole  //,  and  on  to  the  under  side  of  the  shaft 
through  the  hole  in  the  disk  BD.  To  insure  a  continuous  flow 
of  oil  through  the  holes,  grooves  are  made  on  the  under  side 
of  the  journal-box,  and  upon  the  upper  side  of  the  projection 
upon  which  the  disk  BD  is  carried.  To  prevent  lateral  motion 
the  end  of  the  shaft  is  turned  to  fit  the  journal-boxy,  which 
is  provided  with  a  brass  bush  (B).  The  bush  is  secured 
against  turning  with  the  shaft  by  the  projections  E,  which  fit 
between  lugs  cast  on  the  inner  surface  of  the  journal-box. 
The  under  side  of  the  journal-boxy  is  slightly  spherical  and 
rests  upon  a  surface  which  is  also  slightly  spherical.  This 
allows  the  journal-box  to  be  tipped  over  for  a  limited  dis- 
tance by  means  of  the  set-screws  5  until  its  axis  coincides 
with  that  of  the  shaft.  The  down -pressure  of  the  shaft  is 
carried  upon  a  steel  disk  BD,  which  also  rests  upon  a  slightly 
spherical  projection  cast  on  the  upper  side  of  the  journal-box 
bottom, 'allowing  the  whole  of  the  shaft  end  to  remain  in  con- 
tact with  the  disk  although  the  bush  B  has  become  sufficiently 
worn  to  allow  the  shaft  to  have  side  motion,  thus  making  the 
bearing  adjustable,  and  capable  of  maintaining  a  perfect  bear- 
ing over  its  entire  surface  under  all  ordinary  working  con- 
ditions. The  disk  BD  is  longer  than  the  shaft  diameter,  and 
is  prevented  from  turning  with  the  shaft  by  the  flat  sides  com- 
ing in  contact  with  the  lugs  /.  The  journal-box  is  hexagonal 


ENGINE   DETAILS. 


350  DRAWING   AND   DESIGNING. 

in  cross-section,  and  is  tapered  towards  the  top  to  allow  it  to 
tip  the  required  distance  without  increasing  the  diameter  of 
the  oil-basin.  It  is  held  against  turning  with  the  shaft  by  the 
set-screws  .S  pressing  against  the  flat  faces.  This  form  of 
pivot  or  step  bearing  is  suitable  for  journals  from  \\"  to  3^" 
in  diameter. 

As  the  velocity  of  the  bearing  surface  varies  from  zero  at 
the  centre  to  a  maximum  at  the  circumference,  and  as  the 
friction  increases  with  the  velocity,  the  wear  will  increase  from 
the  centre  to  the  circumference.  Thus  it  will  be  seen  that 
the  smaller  the  diameter  D  of  the  journal,  within  limits  deter- 
mined by  the  pressure  per  square  inch  on  the  rubbing  sur- 
faces', the  more  will  the  tendency  to  wear  be  reduced. 

D  will  be  found  by  the  formula 


from  which 


(I) 


where  P  =  intensity  of  pressure  per  square  inch  of  projected 
area,  which  with  this  form  of   bearing  running 
continuously  may  be  taken  at  300  Ibs.  ; 
T=  total  load  on  the   rubbing  surface,   which  is  the 

weight  of  the  shaft  and  its  attachments. 
Exercise  136.  —  Design  a  bearing  of  the  form  shown  in  Fig. 
278,  to  carry  a  load  of  1450  Ibs.  Show  a  HALF  ELEVATION, 
a  HALF  SECTIONAL  ELEVATION,  a  SECTIONAL  END  VIEW,  the 
planes  of  section  passing  through  the  centre  of  the  bearing, 
a  HALF  PLAN  and  a  HALF  SECTIONAL  PLAN,  the  plane  of  sec- 


ENGINE   DETAILS.  35  ! 

tion  passing  through  the  bearing  at  the  line  ab.  The  unit  of 
proportions  =  /?  +  £''.  The  thickness  t  of  the  brass  bush, 
and  the  bearing  disk  at  the  centre  may  be  made  =  .oSD  +  Ty . 
The  parts  dimensioned  in  inches  are  constant  for  all  sizes  of 
j o  u  rnals.  Scale  full  size. 

Crank-shaft  or  Main  Bearings. — The  bearings  carrying 
the  crank-shaft  of  a  vertical  engine  have  the  greatest  pres- 
sure acting  nearly  vertically ;  consequently  the  greatest  wear 
will  be  above  and  below  the  shaft,  and  adjustment  is  effected 
by  a  two-part  bearing,  parted  on  the  horizontal  centre  line, 
as  in  Fig.  170.  The  crank-shaft  bearings  of  horizontal 
engines  should  be  designed  for  horizontal  adjustment  to  take 
up  the  side  wear  caused  by  the  pull  and  thrust  transmitted 
along  the  connecting-rod,  and  vertically  to  take  up  that 
caused  by  downward  pressure  due  to  the  weight  of  the  fly- 
wheels, etc.  Vertical  and  horizontal  adjustment  can  be 
obtained,  with  a  two-part  bearing,  by  parting  the  bushing 
at  an  inclination  with  the  direction  of  both  pressures.  The 
inclination  is  generally  mad-  at  45°.  The  frame-work  con- 
nected with  the  crank  bearings  on  horizontal  engines  is 
generally  part  of  the  engine  frame,  as  in  Figs.  279  and  280. 

Three-part  Bearing — An  example  of  this  form  of  bearing 
is  shown  in  Fig.  279,  where  the  horizontal  wear  is  taken  up  in 
one  direction  only,  by  screwing  in  the  screws  A,  which  move 
up  the  adjusting-gibs  G  against  the  shaft.  The  vertical  wear 
is  taken  up  by  screwing  down  the  cap  C.  In  this  design,  as 
the  bearings  wear,  the  shaft  will  be  moved  forward  and  down, 
and  can  only  be  returned  to  its  original  position  by  renewing 
the  babbitt  strips.  The  cap  is  made  to  fit  into  the  frame,  and 
is  also  provided  with  projections  which  fit  over  the  outside  of 


352 


DRA  WING   AND   DESIGNING. 


the  frame,  thus  insuring  that  it  will  sit  squarely  upon  its  jour- 
nal.    To  keep  the  cap  (C)  from  being  screwed  too  far  and 


FIG.  279. 

clamping  the  shaft,  it  is  provided  with  an  adjusting-screw  at 
each  corner. 

The  lubricator  O  consists  of  a  pocket  cast  in  the  cap  from 
which  the  oil  is  conveyed  to  the  bearing  through  the  holes  H. 
These  are  filled  with  cotton  to  keep  the  oil  from  flowing  into 
the  bearing  too  rapidly.  This  system  of  lubrication  is  efficient, 


ENGINE  DETAILS.  353 

but  very  wasteful  unless  the  surplus  oil  flowing  from  the  bear- 
ing can  be  caught  and  used  again.  This  is  done  (Fig.  279) 
by  casting  a  hollow  projection  OC  on  the  frame  under  the 
bearing,  from  which  the  oil  is  drained  off  by  the  pipe  OP  to 
the  bottom  of  the  engine  frame. 

Four-part  Bearing. — This  form  of  bearing  (Fig.  280)  is 
parted  on  each  quarter  of  the  journal,  which  allows  the  wear, 
caused  by  the  thrust  and  pull  on  the  connecting-rod,  to  be 
taken  up  on  either  side.  This  is  effected  by  screwing  down 
the  bolts  Aj  which  pull  up  the  tapered  wedges  W,  moving  the 
gibs  C  forward  toward  the  journal.  To  hold  the  bolts  A 
against  turning  back,  they  are  provided  with  a  locking  arrange- 
ment, shown,  drawn  to  an  enlarged  scale,  in  Fig.  281.  The 
vertical  adjustment  is  obtained  by  screwing  down  the  cap- 
bolts  CB.  The  under  side  of  the  journal  is  carried  upon  a 
block  LB,  which  is  allowed  to  move  transversely,  thus  allow- 
ing it  to  adjust  itself  to  the  journal,  but  is  held  against  moving 
longitudinally  by  projections  which  fit  over  the  raised  part 
F on  the  frame.  The  top  bearing  TB  is  held  in  position  by 
the  screws  S,  which  also  serve  to  hold  the  gibs  (G)  in  position 
and  keep  the  cap  from  being  screwed  down  too  tightly  on  the 
shaft.  The  lubricator  O  may  be  used  for  semi-liquid  grease 
or  by  filling  it  with  cotton  saturated  with  oil. 

Length  of  Crank  Bearing. — To  calculate  the  length  of  a 
bearing  it  is  necessary  that  we  should  know  the  amount  and 
direction  of  the  pressure  to  which  it  is  subjected.  The  pres- 
sure on  the  crank-shaft  bearings  of  a  horizontal  engine  is 
uncertain  in  amount  and  direction.  We  can  determine  the 
amount  and  direction  of  the  resultant  pressure  caused  by  the 
thrust  and  pull  of  the  connecting  rod  and  that  due  to  the 


354  DRAWING   AND    DESIGNING. 

weight  of  the  fly-wheels  and  shaft,  but  this  pressure  may  be 
either  augmented  or  relieved  by  the  transmission  of  the 
power. 

A  reliable  rule,  and  one  which  is  generally  observed  in 
this  country,  is  to  make  the  length  of  the  bearing  equal  to 
TWICE  THE  DIAMETER  OF  THE  SHAFT. 

The  Cap.—  To  relieve  the  cap  as  much  as  possible  from 
the  stresses  the  frame  is  carried  up  well  around  the  bearing, 
and  the  cap  (C)  is  practically  a  flat  plate.  The  upward  pres- 
sure of  the  cap  caused  by  the  angularity  of  the  connecting-rod 
is  found  by  the  formula 

P 


This  pressure  may  be  augmented  by  the  gearing  which  is 
used  to  transmit  the  power,  and,  to  insure  that  the  cap  and 
cap-studs  will  have  sufficient  strength  under  the  worst  condi- 
tions, the  value  of  p  should  be  increased  \oofc.  Then  the 
maximum  pressure/'  on  the  cap  will  be  found  by  the  formala 


<'> 


where  P  —  total  steam-pressure  on  the  piston  ; 

R  —  ratio  of  length  of  connecting-rod  to  throw  of  crank. 
The  length  of  connecting-rod   is  generally  made  equal  to 
6  times  the  throw  of  crank.      The  cap  is  in  the  condition  of  a 
beam  on  which  the  load  is  distributed  over  its  entire  surface. 

Then  the  bending  moment  is  ~,   and  the  moment  of  re- 

o 

LT* 
sistance  to  bending  is  —?—/•     Therefore 

#'r  ••££'; 

8  "      6   7> 


ENGINE   DETAILS.  355 

from  which 


;    //x/xe 

•  V  L  X  8  X/' 


where  L  =  length  of  cap ; 

T  =  thickness  of  cap ; 
p'  =  total  load  on  cap; 
/=  distance  between  cap-studs; 
/=  strength  of  the  material,  which  may  be  taken  at 

5000  Ibs. 

Diameter  of  Studs. — The  maximum  pressure  (/')  on  the 
under  side  of  the  cap  is  resisted  by  the  studs  CB.  There- 
fore their  effective  area  will  be  found  by  the  formula 

Area  at  bottom  of  thread  =  — , 


where  n  =  number  of  studs ; 

ft  =  strength  of    material  =  5000   Ibs.  per  square  inch 
of  area  at  bottom  of  threads. 

Having  found  the  area  at  the  bottom  of  the  threads,  turn  to 
Table  No.  8,  page  66,  from  which  take  the  nearest  diameter 
of  screw  having  the  required  area.  The  diameter  of  the 
adjusting-studs  (A)  and  the  set-screws  (s)  may  be  made  f 
in  diameter  when  the  journal  is  6"  or  less,  and  increased 
•§•"  for  every  inch  the  journal  is  increased  above  6"  in 
diameter. 

The  Gibs. — The  height  of  the  gibs  (G)  should  be  f,  and 
their  thickness  at  /  should  be  equal  to  £,  of  the  shaft 
diameter. 

Adjusting-wedges. — Instead  of  using  three  adjusting 
wedges  and  screws,  as  in  Fig.  280,  another  arrangement  is  to 


DRAWING  AND   DESIGNING. 

use  one  wedge  and  one  adjusting-screw  with  two  guide-pins, 
as  in  Fig.  282.  In  the  latter  arrangement  the  wedge  sup- 
ports the  gib  and  is  in  contact  with  the  frame  its  entire  length. 
The  thickness  of  the  wedges  at  the  top  should  be  I J  times 
":he  diameter  of  the  screw  (A)  -f  i",  and  their  width  w  when 


FIG.  282. 


FIG.  280. 


FIG.  28 i 


three  are  used  should  not  be  less  than  \  the  length  of  the 
journal  (L).  The  taper  of  the  wedges  may  be  made  from  I 
in  6  to  I  in  8.  The  screw  A  should  be  sufficiently  long  to 
enter  the  wedge  W  a  distance  equal  to  its  diameter  when  the 
wedge  is  full  down. 

Top  and  Bottom  Blocks. — The  thickness  t  at  the  thin- 
nest part  of  the  bottom  block  should  be  equal  to  .23,  and 
that  of  the  top  block  .15,  of  the  journal  diameter. 


ENGINE  DETAILS.  357 

Exercise  137. — Design  a  crank-shaft  bearing  of  the  form 
shown  in  Fig.  279,  proportioned  for  a  horizontal  steam- 
engine,  having  a  cylinder  9"  in  diameter,  stroke  10",  initial 
steam-pressure  200  Ibs.  per  square  inch,  and  the  diameter  of 
the  journal  (D)  4".  The  bearing  to  have  a  vertical  and  hori- 
zontal adjustment  of  f".  Show  a  HALF  ELEVATION,  A  HALF 
SECTIONAL  ELEVATION,  a  HALF  END  VIEW,  a  HALF  SECTIONAL 
END  VIEW,  a  HALF  PLAN,  and  a  HALF  SECTIONAL  PLAN  of 
the  right-hand  side.  Scale  8"  to  the  foot. 

Exercise  138. — Design  a  crank-shaft  bearing  of  the  form 
shown  in  Fig.  280,  proportioned  for  a  horizontal  steam- 
engine  having  a  cylinder  18"  in  diameter,  stroke  30"  long, 
and  an  initial  steam-pressure  of  220  Ibs.  per  square  inch, 
The  bearing  to  have  a  horizontal  adjustment  of  J"  in  either 
direction  and  a  vertical  adjustment  of  $•" '.  Make  D  the 
diameter  of  the  journal  9". 

Show  an  ELEVATION,  PART  PLAN,  and  PART  SECTIONAL 
PLAN,  the  plane  of  section  passing  through  the  centre  of 
journal.  Scale  4."  to  the  foot. 

Show  also  a  detail  drawing  of  the  adjusting  screws  and 
wedges,  as  in  Fig.  281.  Scale  8"  to  the  foot. 

Exercise  139 — Design  a  crank-shaft  bearing  of  the  form 
shown  in  Fig.  280,  substituting  the  adjusting-wedge  arrange- 
ment shown  in  Fig.  282.  Make  the  proportions  suitable 
for  the  conditions  given  in  Exercise  138.  Scale  4!'  to  the  foot. 

Ball  Bearings. — This  device  for  reducing  friction  consists 
of  perfect  spheres  placed  between  the  journal  and  the  bear- 
ing; the  balls  taking  the  place  of  the  bush  in  supporting  the 
shaft,  thus  substituting  rolling  for  sliding  friction.  As  the 
bearing  areas  are  only  slightly  flattened  points,  the  wear  will 


35°  DRAWING   AND   DESIGNING. 

be  comparatively  rapid ;  so,  to  reduce  the  amount  to  a 
minimum,  the  balls  and  the  surfaces  upon  which  they  roll 
are  made  of  steel  tempered  as  hard  as  possible. 

The  different  forms  of  ball  bearings  are  designated  accord- 
ing to  the  number  of  points  that  the  balls  have  in  contact 
with  the  surfaces  upon  which  they  roll. 

In  a  three-point  bearing  a  line  drawn  through  one  of  the 
points  in  the  direction  in  which  the  load  acts  should  pass 
midway  between  the  other  two  points.  Thus  the  form  of 
bearing  shown  in  Fig.  283  will  give  good  results  only  when 
the  resultant  of  all  the  pressures  acts  at  an  angle  of  45°,  other- 
wise the  balls  will  not  revolve  on  a  true  axis,  but  will  have  a 
screw  motion  and  therefore  a  considerable  amount  of  friction. 
The  design  shown  in  Fig.  284  is  suitable  for  a  pressure  in  a 
vertical  direction  only.  In  a  four-point  bearing  a  line  drawn 
through  one  of  the  points  in  the  direction  in  which  the  pres- 
sure acts  should  pass  through  a  contact-point  on  the  other  side 
of  the  ball  (as  in  Fig.  285),  then  the  balls  revolve  on  a  true 
axis  and  sliding  friction  is  entirely  avoided. 

Size  of  Balls. — Steel  balls  rolling  under  pressure  do  not 
fail  by  crushing,  their  period  of  usefulness  depending  upon 
both  speed  and  pressure.  This  would  seem  to  indicate  that 
the  balls  should  be  as  large  as  possible,  thus  reducing  the 
number  of  revolutions  in  proportion  to  those  of  the  shaft,  and 
increasing  their  strength;  but' there  is  a  practical  limit  to  this 
owing  to  the  fact  that  the  larger  the  balls  the  fewer  will  be 
the  number,  and  therefore  the  fewer  the  number  of  bearing 
points.  The  bearing  would  then  fail  by  the  balls  crushing 
into  the  surfaces  upon  which  they  roll.  There  is  a  great  di- 
versity of  opinion  as  to  the  proper  size  of  ball  in  relation  to 


ENGINE  DETAILS. 


359 


load  and  speed.  The  size  given  in  Table  No.  37  gives  a  fair 
average  proportion  of  the  diameter  of  the  ball  to  the  diameter 
of  shaft  used  in  practice  for  horizontal  bearings. 


TABLE   NO.    37. 


Shaft  Diam. 

Ball  Diam. 

Crushing  Strength 
of  Ball. 

Shaft  Diam 

Ball  Diam. 

Crushing  Strength 
of  Ball. 

i 

" 

TV 
ft 

|  '  ...".  3  000 

;|" 

i" 

j-         20000 

j-            5000 

2 

| 

h         30000 

•j 

ft 

7000 

3 

f 

40  8OO 

jj 

f 

!•          12000 

si 

4 

I 

50000 
60000 

Ball  Races. — The  thickness  (/)  of  the  surfaces  upon  which 
the  balls  roll  should  not  be  less  than  J  the  diameter  (d)  of  the 
ball,  and  the  width  W=  i£  times  the  ball  diameter.  The 
angles  of  the  grooves  are  generally  made  45°.  In  every  ball 
race  a  slight  amount  of  clearance  (c)  is  left  between  each  pair 
of  balls.  This  is  necessary,  first  to  get  the  balls  into  place, 
second  to  insure  the  free  rolling  of  the  balls.  The  amount  of 
clearance  is  generally  made  from  .002  to  .004;  it  will  there- 
fore be  safe  to  assume  .003  as  good  practice.  Then  taking  the 
diameter  Dl  of  the  ball  circle  =  D  +  2t  +  d  =  D  +  2d.  In 

360°        

Fig.  285  the  angle  $0  =  -     -  =  — 


211 


1 80  I  80° 

sin  - 
n  n 


d+c 
-~ 


From    a   table   of  sines   find  the  angle  6  in  degrees  corre- 
sponding to  x.     Then 

i  80°  i  80° 


=  x       and 


n  = 


(4) 


The  number  of  balls  must  be  within  .001  X  n  of  being  a 
whole  number;  if  not,  we  must  increase  the  diameter  Z?,.    Thus 


360 


DRAWING   AND   DESIGNING. 


supposing  that  formula  No  4  gives  n  =  20.75,  then  we  must 
increase  D^  to  get  in  the  next  whole  number  of  balls. 
Taking  n  =  21,  we  can  find  Z>,  by  the  formula 


A  = 


sin 


I8o< 


(5) 


Load  on  Bearings. — As  already  explained,  the  life  of  a 
bearing  is  a  function  of  both  speed  and  load.     Therefore  if 


FIG.  283. 


FIG.  284. 


FIG.  286. 


A4U& 


FIG.  285. 

the  speed  is  increased,  the  load  must  be  correspondingly  de- 
creased or  the  life  of  the  bearing  will  be  shortened.  Using 
the  proportion  of  ball  to  the  shaft  diameter  given  in  Table 


ENGINE  DETAILS.  361 

37,  the  safe  load  in  relation  to  the  speed  may  be  found  by 
the  formula 

r  _/cX    N 

L-—^<      '     •     •    '    •    •     (6) 

where  L  =  total  load  on  the  bearing; 
fe  —  strength  of  ball; 

5  =  speed  of  the  ball  races  in  feet  per  minute ; 
N=  number  of  balls  carrying  the  load ;   in  horizontal 
bearings  =  i  of  the  total  number. 

Exercise  140. — Design  a  lathe  grinder  of  the  form  shown 
in  Fig.  286  provided  with  four-point  ball  bearings.  Make 
the  emery-wheel  6"  in  diameter  Xj"  thick,  belt  drum  ij"  in 
diameter  and  length  suitable  for  a  ij"  belt.  The  diameter 
of  the  shaft  (D)  =  f  ". 

Show  an  ELEVATION  with  one  of  the  bearings  partly  in 
section,  a  HALF  END  VIEW  and  a  HALF  SECTIONAL  END  VIEW 
as  shown  in  Fig.  286.  Scale  twice  full  size. 

Thrust  Bearings._The  difficulty  experienced  with  the 
ordinary  pivot  or  thrust  bearing,  due  to  the  velocity  increas- 
ing as  the  distance  from  the  centre,  is  overcome  by  the 
application  of  balls  to  this  type  of  bearing.  The  designs 
shown  in  Figs.  287  and  288  are  made  by  the  Boston  Ball 
Bearing  Co.  and  may  be  used  on  either  vertical  or  horizontal 
shafts.  The  balls  are  held  in  place  by  the  cage  C,  the  use  of 
which,  although  tending  to  increase  rather  than  diminish  fric- 
tion, facilitates  the  placing  and  removing  of  the  balls,  and  by 
its  use  the  balls  can  be  placed  at  various  distances  from  the 
centre  cf  the  shaft,  thus  increasing  the  time  the  bearing  will 
run  before  wearing  grooves  in  the  plates  PB.  In  Fig.  288 


362 


DRA  WING   AND   DESIGNING. 


the  balls  are  arranged  in  spirals ;  thus  every  ball  runs  on  a 
separate  path,  and  the  tendency  to  wear  grooves  is  reduced  to 
a  minimum.  The  small  cages  are  made  in  one  piece,  as  in 
Fig.  287,  and  the  balls  are  put  into  position  by  springing  the 
cage,  while  in  the  large  cages  the  top  is  fastened  to  the  under 
side,  by  rivets,  after  the  balls  are  in  position,  as  in  Fig.  288. 
The  cages  are  made  from  f%"  to  \"  thick.  The  thickness  (t) 
should  not  be  less  than  £  the  diameter  of  the  ball,  and  the 


DR 


FIG.  288. 


FIG.  287. 


distance  e  should  not  be  less  than  £  of  the  ball  diameter. 
The  centres  of  the  ball  races  are  J  of  a  ball  diameter  apart. 
The  hub  H  is  screwed  to  the  shaft  by  means  of  one  or  more 
set-screws  (5),  the  diameter  of  which  may  be  made  .2D,  but 
not  greater  than  J".  L  =  2t  +  3*/,  but  not  less  than  %D. 
g  =  .12D. 

D'  =  2D  when  D  is  less  than  2",  and  =  1.7  when  D  is  2" 
or  over.  The  load  and  speed  to  which  this  type  of  bearing  is 
subjected  will  determine  the  number  of  balls.  Taking  the  size 


ENGINE   DETAILS. 


3<53 


of  ball  in  proportion  to  the  diameter  of  the  shaft  from  Table 
No.  37,  then  from  formula  No.  6 

L  X  S 

fc 

Exercise  141. — Design  a  thrust  bearing  of  the  form  shown 
in  Fig.  287  for  a  4"  shaft,  to  carry  a  load  of  760  Ibs.  and  run 
at  a  speed  of  600  revolutions  per  minute.  Scale  full  size. 

Stuffing-boxes. — To  prevent  leakage,  when  rods  work 
through  the  walls  of  a  chamber  containing  fluid,  the  rod  is 
passed  through  a  cavity  filled  with  an  elastic  material  which 
will  adjust  itself  to  any  irregularities  on  the  surface  of  the 
rod.  Fig.  289  shows  a  stuffing-box  suitable  for  a  horizontal 


FIG.  289. 

steam-engine   piston-rod?  and    Fig.    290  one  arranged   for  a 
vertical  steam-engine  piston-rod.  * 

The  stuffing-box  SB  may  be  made  a  separate  piece  and 
bolted  to  the  cylinder-head,  as  in  Fig.  289,  or  cast  with  the 
cylinder-head,  as  in  Fig.  290.  Part  of  the  box  SB  is  bored 


DRAWING   AND   DESIGNING. 


FIG.  290. 


ENGINE  DETAILS.  365 

larger  than  the  diameter  of  the  piston-rod  PR,  thus  leaving  a 
space  5  around  the  rod  which  is  filled  with  packing  consisting 
of  a  fibrous  material  saturated  with  oil  or  tallow.  The  pack- 
ing is  pressed  against  the  rod  by  screwing  down  the  gland  G, 
which  is  generally  made  of  brass  for  rods  under  4"  in  diam- 
eter, as  in  Fig.  289,  and  of  cast  iron  lined  with  brass  for 
the  larger  rods,  as  in  Fig.  290. 

Proportions.  —  The  proportions  of  the  stuffing-box  are 
generally  decided  by  the  conditions  under  which  it  is  used  ; 
thus  the  box  is  generally  made  longer  for  a  high  than  a  low 
pressure.  However,  under  any  conditions,  the  longer  the 
box  the  longer  will  the  packing  last. 

The  following  proportions  are  suitable  for  average  pres- 
sures and  speeds,  and  could  be  used  for  high  pressure,  but 
would  require  to  be  repacked  comparatively  often  : 

L  =  2D  for  rods  2"  or  less  in  diameter; 
L  =  \\D  for  rods  between  2"  and  3"  in  diameter; 
L  =  \\D    "      "  "        3"    "    4"  "        "         ; 

L  =  D  +  i  "  for  rods  over  4"  in  diameter  ; 

/,  =  .7$L  ;      T  =  \D  in  nearest  T^  ;  . 
/?'=  =  1.75/7  +.25;  /=.5/?  +  i"; 

d=  .2D;  r 

C=  \\D-\-2d;  £ 


R  =  2D;  d'  =.  from  f"  to  J". 

Exercise  142.  —  Draw  a  stuffing-box,  in  which  soft  packing 
is  to  be  used,  for  a  horizontal-engine  piston-rod  (Fig.  289). 
Make  D  =  i%"  in  diameter.  Scale  full  size. 

Exercise  143  —  Draw  a  stuffing-box  (Fig.  290),  in  which 


366  DRA  WING   AND   DESIGNING. 

soft  packing  is  to  be  used,  for  the  H.-P.  cylinder  of  a  vertical 
steam-engine.  Make  D  =  4" '.  Thickness  of  cylinder-cover 
1 1".  Scale  8"  to  the  foot. 

Metallic  Packing. — Many  designs  of  metallic  packings 
have  been  devised  to  replace  the  soft  packings.  One  of  the 
most  successful  is  that  known  as  the  United  States  Metallic 
Packing.  A  design  showing  the  application  of  this  form  of 
packing  suitable  for  high-pressure  steam-engine  piston-rods  is 
shown  in  Fig.  291.  This  form  is  known  as  the  "double 
packing"  and  is  practically  two  sets  of  the  ordinary  form  of 
packing  arranged  in  tandem.  In  Fig.  291  the  back  packing 
is  shown  in  section  and  the  front  partly  in  section.  The 
packing  consists  of  babbitt-metal  rings  A,  B,  and  C  which 
are  cut  in  halves  and  forced  into  the  cup  H  by  the  spiral 
spring  5.  On  the  packing  nearer  the  cylinder  the  spring  S 
will  be  aided  by  the  steam-pressure  acting  on  the  follower  F. 
The  rings  A,  By  and  C  are  conical,  and  being  forced  into 
the.  correspondingly  shaped  cup  //,  the  cup-rings  close  and 
press  against  the  piston-rod  PR.  The  cup  H  rests  against 
the  flat  face  of  the  ring  R,  which  forms  a  ball-and-socket 
joint  with  the  outer  casing  G  or  preventer  P' .  As  the  cup 
H  is  free  to  slide  on  the  flat  face  of  the  ring  R,  which  in 
turn  is  free  to  rock  on  the  casing  G  or  P' ,  the  packing  never 
binds  the  rod  nor  constrains  it  in  any  way.  The  packing  is 
prevented  from  drawing  back  with  the  rod  (beyond  a  small 
movement)  by  the  flange  on  the  follower  F  coming  in  contact 
with  the  preventer  P  or  P1 '. 

Exercise  144. — Draw  the  arrangement  of  United  States 
Metallic  Packing  shown  in  Fig.  291.  Scale  full  size. 


ENGINE  DETAILS. 


mm  A  Ba,Cnwt 
IH  HALVES  wrmit  CUTOUT 

SPRINGS +&  OUTSIDE  DUM» 

4 cms  ii 


D.  R. 


FIG.  291. 


368 


DRAWING   AND   DESIGNING. 


Cross-heads  and  Guides. — When  the  connecting-rod  is 
inclined  toward  the  direction  in  which  the  piston  is  moving  it 
will  exert  an  upward  or  downward  pressure  according  to  the 
direction  in  which  the  engine  is  running,  and,  unless  special 
means  are  employed,  would  tend  to  bend  the  piston-rod  or 
force  it  out  of  its  straight  path.  To  prevent  such  an  occur- 
rence the  piston-rod  end  is  provided  with  a  cross-head  which 


R 


FIG.  292. 


slides  on  surfaces  that  are  parallel  with  the  piston-rod,  called 
guides. 

Cross-head  Blocks. — Assuming  that  steam  is  not  cut  off 
before  midstroke,,then  the  thrust  caused  by  the  obliquity  of 
the  connecting-rod  will  reach  a  maximum  when  the  crank  is 
nearly  at  right  angles  with  the  line  BO  (Fig.  292). 

Taking  L  —  load  on  piston ; 

R  =  thrust  of  the  connecting-rod ; 
/  =  steam-pressure  per  square  inch ; 
/'  =  intensity  of  pressure  per  square  inch ; 
V=  velocity  of  cross-head  in  feet  per  minute; 
A  =  area  of  the  bearing-surface  in  square  inches, — 


then 


L:  R:\BO\AO. 


ENGINE  DETAILS.  369 

Therefore 

AO  AO 


E>  _     7"    vx    —    T    y 

A  BO  "    "  A   V^^1  —  ^6>8' 
Taking  the  length  of  the  crank  OA  as  the  unit,  then 


I  L 

r>  _.     r  ^ 


where  n  =  ratio  of  connecting-rod  to  crank. 

Pressure  on  Rubbing-surfaces.  —  There  is  great  diver- 
sity of  opinion  as  to  the  proper  intensity  of  pressure  on  the 
guide-blocks.  It  varies,  according  to  the  different  authori- 
ties, from  22  to  500  Ibs.  per  square  inch.  Thurston  gives 

40000 
ti'  =  —  J7~*    anc*  tnat    this  value   in   marine    and   stationary 

engines  may  be  exceeded  to  the  extent  that/7  =  60000  -f-  V. 
Then 


40000       40000  (iV—  i) 

In  many  cases  of  ordinary  stationary-engine  practice, 
especially  on  engines  having  four-bar  guides,  the  above 
formula  would  give  a  very  short  block,  and  as  there  is  gener- 
ally no  difficulty  in  providing  large  rubbing-surfaces,  we  find 
the  areas  increased  as  large  as 

A  =  R^,     ......     (8) 

25000 

where  F=  velocity  of  piston  in  feet  per  minute  =  (length  of 
stroke  X  twice  the  number  of  revolutions  per  minute). 

The    cross-head  should  always  be  designed    so   that   the 


37°  DRAWING     IND   DESIGNING. 

resultant  pressure  (K)  on  the  guides  will  have  its  point  of 
resistance  at  the  centre  of  the  cross-head  rubbing-surfaces,  as 
shown  in  Fig.  292. 

Wrist-pin. — The  connecting-rod  is  attached  to  the  cross- 
head  by  the  pin  CP,  Fig.  293.  In  this  form  of  joint,  as  the 
velocity  is  low  and  the  pressure  constantly  changing  in  direc- 
tion and  magnitude,  the  allowable  pressure  per  square  inch  is 
comparatively  high,  reaching  in  some  designs  as  much  as 
1400  Ibs.  per  square  inch.  Seaton  says  that  the  pressure  per 
square  inch  should  never  exceed  1200  Ibs.  per  square  inch  of 
projected  area  (d  X  /)• 

When  the  total  load  on  the  pin  is  taken  as  the  maximum 
load  on  the  piston,  i.e.,  the  initial  steam-pressure  X  area  of 
piston,  the  length  of  the  pin  is  generally  made  to  equal  from 
d  to  1.3^. 

Taking  the  length  /  =  </,  then 


p 

When  the  length  of  the  pin  is  made  equal  to  f  of  its  diameter, 
then 


Taking  the  value  of/'  =  1200,  then 

d—   VL-^-^o     and      /  =   VL  ~  30.    .      .     (10) 

A  pin  proportioned  to  either  of  the  above  formulae  will  be 
amply  strong  to  resist  bending. 

Guide-bars. — When  the  guiding-surfaces  are  part  of  the 
frame  the  guides  are  bored  and  the  bearing-surfaces  on  the 
cross-head  are  turned  as  in  Fig.  297.  This  arrangement 


ENGINE   DETAILS. 


371 


3/2 


DRAWING   AND    DESIGNING, 


reduces  the  number  of  parts,  which  is  always  a  good  point  in 
designing,  as  it  not  only  decreases  the  labor  but  also  the 
liability  to  error  in  fitting  up.  When  made  separate  the  bear- 
ing-surfaces are  flat,  and  the  guide-bars  are  generally  of  rect- 
angular (when  of  steel)  or  T  section  (when  of  cast  iron). 

To  prevent  the  formation  of  ridges,  due  to  the  travel  of 
the  cross-head  varying  as  the  wear  on  the  connecting-rod 
joints  is  taken  up,  grooves  are  cut  across  the  bars  over  which 
the  ends  of  the  cross-head  blocks  (CB)  project  at  the  end  of 
each  stroke. 

Strength  of  Guides. — The  greatest  pressure  on  the  bars 
occurs  when  the  cross-head  is  nearly  at  the  centre.  Then  the 

RL' 

bending  moment  is  =~z~  an<3  the  moment  of  resistance  to 

bending  =  fZ.  Where  Z  is  the  modulus  of  section,  given  in 
Table  No.  29. 

The  Length  of  Guide-bars  between  distance-pieces  is 
=  to  the  stroke  +  the  length  of  the  block  -f-  end  clearance, 
which  may  be  made  =  i"  at  each  end. 

Four-bar  Guide. — The  arrangement  shown  in  Fig.  293  is 
that  used  on  the  cycloidal  engine  (Atlas  Engine  Works). 


CP 

U-  - 

1 

DR 

FIG.  294. 

With  this  arrangement  the  pressure  Pis  equally  distributed  on 
each  side  of  the  piston-rod,  which  is  guided  laterally  as  well 
as  vertically  by  the  cross-head  sliding  on  the  inner  surfaces  of 


ENGINE  DE7*AILS.  3/3 

the  guide-bars  G.  The  piston-rod  PR  is  secured  to  the  cross- 
head  C  by  the  arrangement  shown  in  Fig.  294.  To  prevent 
the  piston-rod  from  exerting  undue  pressure  on  the  stuffing- 
boxes,  should  the  axis  of  the  piston-rod  not  coincide  with  that 
of  the  cross-head,  the  hole  through  the  shank  of  the  cross- 
head  is  made  larger  than  the  diameter  of  the  piston-rod, 
which  is  adjustable  and  held  in  position  by  means  of  the  set- 
screws  5.  In  this  arrangement  the  breadth  b  of  the  bearing- 
surfaces  on  each  bar  is  generally  made  equal  to  £  their  length. 
The  area  of  the  bearing-surfaces  may  be  determined  by 
formula  No.  8.  Then 


4  O 

The  form  of  guide-bar  used  in  this  design  may  be  made  of 
cast  iron  or  steel,  and  proportioned  in  the  following  manner : 

Having  determined  the  breadth  b  and  the  length  L, 
then  calculating  for  a  bar  of  rectangular  section,  secured  at 
both  ends  and  loaded  at  the  centre,  the  height  h  <A  the  bar  at 
the  centre  will  be  found  by  the  equation 

RL'  _      btf_ 
from  which 


,  XL'X6 


where  f  may  be  taken  at  3000  for  cast  iron,  and  6000  for  steel. 
Take  h'  =  .75  h,  then  the  area  of  the  web  will  be  = 
(h  X  b)  —  (A'X  b),  and  taking  the  thickness  /-of  the  web  =  .4^. 
Then  the  height  of  the  web  at  the  centre  will  equal  area  of 
web  -7-  4#. 


374  DRAWING   AND    DESIGNING 

The  greatest  strain  on  the  stud-bolts  B  which  secure  the 
guides  to  the  engine-frame  is  due  to  screwing  up.  They  may 
be  made  =  i  J"  in  diameter.  To  allow  for  any  slight  inac- 
curacy of  workmanship,  the  holes  through  the  bars  are  made 
Ty  larger  than  the  diameter  of  the  bolts  B,  and  the  bars  are 
adjusted  laterally  by  the  screw  S' .  The  bars  are  adjusted 
vertically  by  means  of  the  nut  Nt  shown  in  Fig.  295,  which 
is  screwed  into  the  guide-bar  blocks  GB.  The  rubbing-sur- 
faces are  lubricated  by  oil-cups  screwed  on  to  the  upper  guide- 
bars.  The  oil  is  transmitted  to  the  lower  bars  through  the 
holes  O  on  the  cross-head. 

Exercise  145, — Draw  the  four-bar  guide  and  cross-head 
arrangement  shown  in  Fig.  293  suitable  for  an  engine  having 
a  cylinder  12"  in  diameter  X  15"  stroke.  Initial  steam-pres- 
sure 75  Ibs.  per  square  inch.  Speed  300  revolutions  per 
minute,  and  a  connecting-rod  four  times  the  length  of  the 
crank.  Scale  4"  to  the  foot. 

Draw  also  details  of  the  adjusting-nut  N  and  the  cross- 
head  pin,  and  show  the  arrangement  of  fastening  the  piston- 
rod  to  the  cross-head,  taking  the  diameter  of  the  piston-rod 
=  2".  Scale  full  size. 

Two-bar  Guide. — When  two  guide-bars  are  used  they  are 
arranged  either  one  above  and  one  below  the  piston-rod  (in 
this  case  a  cross-head  of  the  type  shown  in  Fig.  297  is  used) 
or  both  guide-bars  above  the  piston  as  shown  in  Fig.  296. 
The  latter  arrangement  is  one  commonly  used  in  locomotive 
construction. 

The  pressure  is  on  the  upper  guide,  UG,  when  the  locomo- 
tive is  running  forward,  and  on  the  lower  guide,  LG,  when 
running  back ;  and  as  the  engine  is  generally  run  forward  more 


ENGINE  DETAILS. 


375 


DRAWING   AND   DESIGNING. 

than  back,  the  bearing-surface  on  the  lower  bar  may  be  made 
smaller  than  that  of  the  upper. 

In  this  design  the  cross-head  C  is  of  cast  steel  and  provided 
with  a  brass  slide-block  SB  which  has  strips  of  babbitt  metal 
top  and  bottom.  To  fit  and  remove  the  piston-rod  easily 
from  the  cross-head,  the  shank  is  cut  and,  after  the  rod  is  in 
position,  it  is  gripped  by  screwing  down  the  bolts  CB  and  se- 
cured by  driving  a  tapered  cotter  through  it  and  the  cross- 
head  shank. 

The  hole  O  is  to  allow  for  lubricating  the  cross-head  pin. 
The  guide-blocks  GB  are  fastened  to  the  cylinder  at  one 
end  and  to  a  guide-bar  frame  at  the  other. 

Exercise  146. — Draw  the  cross-head  and  guide-bar  arrange- 
ment shown  in  Fig.  296.  Scale  j"  to  the  foot. 

Also  details  of  the  slide-blocks  SB,  guide-block  GB, 
cross-head  pin  CP,  cotter  C,  and  washer  W.  Scale  half  size. 
Cross-heads. — Adjustments  to  take  up  the  wear  or  for 
original  setting  may  be  accomplished  by  moving  the  guide- 
bars,  as  in  Figs.  293  and  296,  or  the  slide-blocks,  as  in  Fig. 
297. 

In  this  design  the  cross-head  C  is  hollowed  to  receive  the 
connecting-rod  end,  which  works  upon  the  pin  CP.  The  pin 
is  of  case-hardened  steel  and  is  kept  from  turning  by  the 
^-inch  square-headed  screw  K. 

The  piston-rod  PR  is  screwed  into  the  cross-head  and  se- 
cured by  the  nut  LN.  The  socket  into  which  the  rod  PR  is 
screwed  has  flat  surfaces  on  the  top  and  bottom  to  give  clear- 
ance for  the  nut  N. 

The  diameter  at  the  end  of  the  socket  is  equal  to  the  dis- 


ENGINE  DETAILS. 


377 


1 


IJJiJIJ  >. 


3/8  DRAWING   AND  DESIGNING. 

tance  across  the  flats,  and  tapers  back  £  of  an  inch  to  the 
larger  diameter. 

The  bearing-surfaces  on  the  slide-blocks  are  turned,  and 
the  corresponding  surfaces  on  the  frame,  upon  which  they  fit, 
are  bored  to  the  same  radius.  The  blocks  are  provided  with 
grooves  on  the  under  sides,  which  fit  over  projections  on  the 
top  of  the  cross-head,  to  prevent  their  lateral  movement.  To 
take  up  the  wear,  the  slide-blocks  move  horizontally,  on  the 
inclined  surfaces  upon  the  top  and  bottom  of  the  cross-head, 
for  a  distance  equal  to  the  length  of  the  holes  minus  the 
diameter  of  the  studs,  and  by  this  horizontal  motion  they 
move  vertically  T^  of  an  inch. 

Exercise  147. — Draw  a  cross-head  of  the  form  shown  in 

Fig.  297,  showing  a  SIDE  ELEVATION,  END  ELEVATION 
PARTLY  IN  SECTION,  and  a  SECTIONAL  PLAN,  the  plane  of 
section  passing  through  the  centre  of  the  cross-head  pin. 
Scale  full  size. 

Construction. — To  find  the  inclination  necessary  to  give 
the  required  vertical  movement,  mark  off.  on  the  centre  line 
ab  the  distance  from  the  centre  of  the  pin  CP  to  the  point  C, 
and  through  C  draw  the  line  cd  at  right  angles  to  ab  and 
equal  to  the  horizontal  motion  of  the  slide-blocks,  and  through 
d  draw  de  equal  to  the  vertical  movement. 

The  line  drawn  through  the  points  ce  will  have  the  required 
inclination. 

Fig.  298  shows  a  form  of  cross-head  used  on  the  U.  S. 
cruiser  Olympia.  In  this  design  the  wrist-pin  CP  is  outside 
of  the  cross-head,  and  there  are  two  bearing-surfaces  on  the 
connecting-rod  end.  The  slide-blocks  SB  are  secured  to  the 
cross-head  C  by  the  bolts  B.  To  allow  the  removal  of  the 


ENGINE   DETAILS. 


379 


slide-blocks  while  the  cross-head  is  in  position,  one  of  the  pro- 
jecting lips  L  on  each  block  is  removable  and  held  in  place  by 
the  bolts  B.  To  facilitate  the  removal  of  the  piece  L,  it  is 
provided  with  set-screws  S.  The  piston-rod  PR  is  secured  to 
the  cross-head  by  the  nut  shown  in  Fig.  67,  page  100. 

Fig.  299  is  an   isometric  sketch   of   the  complete   cross- 
head. 
FIG.  299. 


FIG.  298. 

Exercise  148. — Draw  a  general  arrangement  of  the  cross- 
head  shown  in  Fig.  299.  Show  a  FRONT  ELEVATION,  a  HALF 
PLAN,  and  a  HALF  SECTIONAL  PLAN  of  the  top,  the  plane  of 
section  passing  through  the  centre  of  the  wrist-pin.  Scale  4. 
incites  to  the  foot. 

Eccentrics. — The  eccentric  is  a  form  of  crank  in  which 
the  radius  of  crank-pin  is  greater  than  the  sum  of  the  radii  of 
the  crank  and  the  shaft,  as  shown  in  Fig.  300,  where  the 


380 


DRAWING   AND    DESIGNING. 


crank  is  shown  by  dotted  lines,  and  the  eccentric  by  full  lines. 
It  is  used  for  converting  circular  into  reciprocating  motion. 
For  this  purpose  its  action  is  identical  with  that  of  a  crank, 
and  as  the  eccentric  absorbs  more  power  than  the  crank 
(owing  to  the  greater  leverage  at  which  the  friction  acts)  it 
is  used  in  preference  only  where  the  throw  is  comparatively 


FIG.  300. 

short.  The  eccentricity  or  throw  of  the  eccentric  is  the 
distance  r  from  the  centre  of  the  shaft  to  the  centre  of  the 
sheave.  The  stroke  of  the  reciprocating  piece  worked  by 
the  eccentric  is  equal  to  twice  the  throw. 

Fig.  301  represents  an  eccentric  used  for  working  the 
slide-valve  of  a  locomotive  engine.  The  eccentric  proper  is 
generally  called  the  sheave  o-  pulley.  When  it  cannot  be 
passed  on  to  position  over  the  end  of  the  shaft,  the  sheave  is 


ENGINE  DETAILS. 


381 


made  in  two  partsT^  and  P',  parted  on  a  line  passing  through 
the  centre  of  the  shaft  and  at  right  angles  to  the  horizontal 
centre  line  of  the  eccentric,  and  held  together  by  studs.  That 


the  strain  may  come  on  the  stronger  part,  /",  the  key  and  set- 
screws  used  in  fastening  the  sheave  to  the  shaft  are  placed  on 
that  part.  The  eccentric-rod  £7?  is  secured  to  the  strap  5  by 


382  DRA  WPNG   AND    DESIGNING. 

the  bolts  £1  B^  B^ .  The  hole  through  the  strap,  for  the 
centre-bolt  B^ ,  is  elongated  that  the  rod  ER  may  be  adjusted 
when  setting  the  valve. 

Proportions.  —  The  thickness  /  of  the  sheave  may  be 
\D  —  £",  with  a  minimum  of  \" .  The  diameter  of  the  sheave 
will  then  =  D  -f-  2r  +  2/.  The  breadth  B  of  the  sheave  may 
be  found  by  the  formula 

L 

=  ^x7' 

where  L  =  load  driven  by  the  eccentric ; 
D'  ==  diameter  of  the  sheave; 

/  =  allowable  pressure   per  square   inch  of  projected 
ft  •=•  area,  which  should  have  a  maximum  of  100  Ibs. 
Thickness  of  key  =  .iD. 
Breadth  of  key  —   i£  times  the  thickness. 
The  size  of  the  strap-bolts  5^  should  be  proportioned  to 
resist  the  load  driven  by  the  eccentric. 


where  d^ •  ===  diameter  at  the  bottom  of  the  threads; 
X:  ±='  load  driven  by  the  eccentric  ; 
f't  =  safe  strength  of  bolts,  which  may  be  taken  at  2000 

Ibs.  per  square  inch. 

The  size  of  the  rod-bolts,  assuming  the  load  is  resisted  by 
the  two  fitted  bolts,  may  be  found  by  the  formula 


d  = 


ENGINE   DETAILS.  383 

f  may  be  taken  at  3000  for  wrought  iron.  The  distance 
C  between  centres  may  be  made  =  ^d'. 

The  parts  marked  in  decimals  are  proportional  to  B,  the 
breadth. 

Exercise  149 — Draw  the  arrangement  of  eccentric-sheave 
and  strap  shown  in  Fig.  301,  proportioned  to  carry  a  load  of 
2300  Ibs.,  taking  the  pressure  per  square  inch  of  projected 
area  =  50  Ibs. 

Draw  the  views  shown  in  Fig.  301 ;  also  a  SECTIONAL  END 
VIEW  looking"  towards  the  right,  the  plane  of  section  passing 
through  the  eccentric  at  the  line  cd.  Make  the  eccentric-rod 
ER  &'  X  1".  Scale  half  size. 


INDEX. 


Aluminum,  33 
Angle,  Lead,  307 
Area  of  a  bearing,  200 

B 

Babbitt  metal,  33 
Ball  bearings,  230 
Base  plates,  Adjustable,  230 
Bearing,  Adjusting  wedges  for,  355 
Bearing,  Area  of  a,  206 
Bearing,  Cap  of,  354 
Bearing,  Chain  lubricating,  225 
Bearing,  Crank-shaft  or  main,  351 
Bearing,  Four-part,  353 
Bearing,  Gibs  for,  355 
Bearing,  Length  of,  235 
Bearing,  Load  on  ball,  360 
Bearing,  Pedestal  or  pillow-block,  230 
Bearing,  Pivot  or  step,  347 
Bearing,  Post,  214 
Bearing,  Solid  journal,  207 
Bearing,  Self-adjusting,  217 
Bearing,  Three-part,  351 
Bearing,  Thrust,  361 
Bearings,  Blocks  for,  356 
Bearings,  Diameter  of  studs  for,  355 
Bearings,  Divided,  210 
Belt  gearing,  238 
Belting,  Rules  for,  240 
Belts,  Length  of,  253 
Belts,  Transmission  of  power  by,  240, 
243 


Bolt,  Anchor,  82 

Bolt,  Hook,  76 

Bolt,  Lewis,  80 

Bolt  of  uniform  strength,  91 

Bolt,  Rag,  78 

Bolt,  Square-headed,  67 

Bolt,  Stud,  68 

Bolt,  Tap,  75 

Bolt,  Tapered,  77 

Bolt,  T-headed,  74 

Brass,  32 

Bronze  or  gun-metal,  32 

Bushes,  steps  or  brasses,  227 

C 

Calking,  126 

Case-hardening,  34 

Castings.  Malleable,  32 

Castings,  Shrinkage  of,  44 

Cast  iron,  30 

Cast  iron,  Specific  gravity  of,  40 

Cast-iron    water-pipe,   Thickness    of, 

43 

Cast  steel,  32 
Cementation  process,  35 
Chilled  castings,  31 
Clearance,  Cylinder,  308 
Clearance,  Inside,  308 
Clearance,  Piston,  308 
Compression,  308 
Cock,  Blow-off,  295 
Cocks,  295 

Connecting-rod,  Thrust  of,  345 
385 


386 


INDEX. 


Connecting-rods,  339 

Connecting-rods,  Buckeye  Engine 
Co.,  341 

Connecting-rods,  Diameter  of,  346 

Connecting-rods,  Erie  City  Iron 
Works,  341 

Connecting-rods,  Marine,  344 

Connecting-rods,  Penn.  Railroad 
Co.'s,  343 

Connecting-rods,  Proportions  of  loco- 
motive, 347 

Constructions,  26 

Conventions,  Standard,  20 

Copper,  32 

Cotter  and  gib,  120 

Cotter  locking  arrangement,  122 

Cotter,  Taper  of,  117 

Cotters,  116 

Couplings,  Box  or  muff,  165 

Couplings,  Cast-iron  pipe,  190 

Couplings,  Converse  pipe,  197 

Couplings,  Flanged  shaft,  178 

Couplings  for  brass  and  copper  pipes, 
203 

Couplings,  Frictional,  174 

Couplings,  Hill  plate,  171 

Couplings,  Jaw  clutch,  181 

Couplings,  Loose  flange,  195 

Couplings,  Pipe,  190 

Couplings,  Propeller  shaft,  185 

Couplings,  Rigid,  164 

Couplings,  Screwed  flange  pipe,  198 

Couplings,  Screwed  socket,  200 

Couplings,  Sellers  clamp,  171 

Couplings,  Shaft,  164 

Couplings,  Spiral  jaw,  181 

Couplings,   Spigot   and    socket    pipe, 

193 

Couplings,  Split  muff,  167 
Couplings,  Stuart's  clamp,  176 
Couplings,  Universal  joint,  185 
Couplings,    Wrought-iron  and    steel- 
pipe,  196 
Cross-heads,  376 
Cross-head  blocks,  368 
Cross-heads  and  guides,  368 
Cross-sections,  26 


Cylinder  flange  fastenings,  69 

Cylinder,  Diameter  of  steam,  328 

Cylinder,  Length  of  steam,  329 

Cylinder,  Steam,  328 

Cylinder,  Thickness  of  steam,  328 

Cylinder  head,  329 

Cylinder  steam-port,  329 

D 

Design,  Elementary  machine,  29 
Design  of  spur  gear,  271 


Eccentrics,  379 

Eccentrics,  Proportions  of,  382 

Eccentric,  Throw  of,  380 

Elasticity,  37 

Elasticity,  Modulus  of,  37 

Elastic  limit,  37 

Engine  details,  305 

Engine-frame  or  bed-plate,  326 

Expansion,  308 


Figuring,  19 

Factor  of  safety,  The,  38 

Frame,  Drop-hanger,  218 


Gearing,  Belt,  238 
Gearing,  Toothed,  262 
Gears,  Bevel,  270 
Gears,  Involute  toothed,  263 
Gears,  Spur-wheel  and  pinion,  268 
Gears,  Walker  system  of,  267 
Gears,  Worm,  271 
Gear-wheels,  Arms  of,  274 
Gear-wheels,  Hubs  of,  276 
Gear-wheels,  Rims  of,  275 
Gear-wheels,  Shrouding  of,  276 
Guide,  Four-bar,  372 
Guide,  Two-bar,  374 
Guide-bars,  370 
Guide-bars,  Length  of,  372 
Guides,  Strength  of,  372 


INDEX. 


387 


Instructions,  Introductory,  I 
Instruments,  7 

J 

Joint,   Forms  and  proportions  of  cot- 
ter, 118 

Joint,  Knuckle,  106 
Joint,  Lap,  143 

Joint,  Locomotive  steam-pipe  ball,  200 
Joints,  Riveted,  125 
Journals,  206. 

K 

Key-heads,  114 

Key,  Flat,  no 

Key,  Round,  112 

Key,  Saddle,  109 

Key,  Sliding  feather,  113 

Key,  Sunk,  no 

Key,  Woodruff,  113 

Keys,  109 

Keys,  Fixed,  112 

Keys,  Strength  of,  114 


Lead,  307 

Lead  angle,  307 

Lettering,  194 

Load,  365 

Locomotive  dome  connection,  156 

Locomotive  fire-box  ring,  154 

Locomotive  plain  slide-valve,  305 

Locomotive  tube-setting,  155 

M 

Malleable  castingss  32 

Materials,  30 

Materials,  Strength  of,  36 

Metallic  packing,  366 

Metallic  packing,  United  States,  366 

Muntz  metal,  32 

N 

Nut  convention,  63 
Nut,  Hexagon,  60 


Nut,  Jam,  92 
Nut-locking  devices,  92 
Nut-lock,  Circular,  99 
Nut-lock,  Spring  washer,  94 
Nut-lock,  Wile's,  95 
sluts  locked  with  set-screws,  96 


0 


Oil-cups,  299 
Overtravel,  308 


Pedestal,  Self-lubricating,  232 

Pin-joint,  Knuckle,  106 

Pins  and  pin-joints,  104 

Pins,  Split,  104 

Pins.  Taper,  105 

Pipes,  189 

Pipes,  Thickness  of,  189 

Piston,  Ball  Engine  Company's,  333 

Piston,  Buckeye  Engine  Company's, 
338 

Piston  clearance,  308 

Piston,  Locomotive,  334 

Piston,  Macintosh  &  Seymour's,  336 

Piston,  Water,  340 

Pistons,  332 

Pistons,  Steam,  332,  335 

Point  of  cut-off,  308 

Pressure  on  rubbing  surfaces,  369 

Projection  of  India-rubber  valv«- 
guard,  282 

Proportions  of  India-rubber  valve- 
guard,  283 

Pulley,  All  wrought-steel,  250 

Pulley,  Cone,  251 

Pulley,  Rope,  255 

Pulley,  Wood  split,  248 

Pulleys,  Proportions  of,  244 

Pulleys,  Proportions  of  cone,  255 

R 

Resistance,  37 

Riveted  butt-joint,  Double,  144 
Riveted  butt-joint,  Triple,  148 
Riveted  joint,  Calculation  of,  136 
Riveted  lap-joints,  Double,  139 


388 


INDEX. 


Rivet-head,  Proportions  of,  130 
Rivet-heads,  Form  of,  128 
Riveting,  Chain,  139 
Rivets  and  riveted  joints,  125 
Rivet-shank,  Length  of,  130 
Rivets,  Pitch  of,  136 


Screw,  Cap,  85 
Screws,  Collar,  85 
Screws,  Holding  power  of,  88 
Screw-thread,   Buttress,  55 
Screw-thread,  Knuckle,  55 
Screw-thread,  Seller's  or  U.  S.  stand- 
ard, 51 

Screw-thread,  Square,  55 
Screw-thread,  Standard  pipe,  56 
Screw-thread,  Whitworth,  53 
Screw-threads,  Conventions  for,  59 
Shade  lines  and  shading,  15 
Shaft,  To  find  diameter  of  steel,  159 
Shaft-couplings,  164 
Shafting,  Deflection  of,  162 
Shafting,  Line,  157 
Shafts,  Hollow,  163 
Sole-plates,  229 
Steel,  Bessemer,  34 
Steel,  Siemens-Martins,  34 
Steps,  227 
Stuffing-boxes,  363 
Strain  and  stress,  36 
Strength  of  cast  iron,  38 
Strength  of  steel,  39 
Strength  of  wrought  iron,  39 
Strength,  Proof,  38 
Strength,  Ultimate,  37 


Table  of  ultimate  and  elastic  strength, 

40 

Table  of  tenacities  of  metals,  40 
Table  of  weights  and  measures,  41 
Table  of  wrought  iron  welded  tubes, 

44 

Table  of  different  colors  of  iron,  45 
Table  of  decimal  equivalents  of  one 

inch,  45 


Table  of  the  melting-point  of  metals, 

etc.,  46 

Table  of  the  weight  of  various  sub- 
stances, 46 

Table  of  the  weight  of  timber,  46 
Table    of    the     circumferences     and 

areas  of  circles,  47 
Table  of  screw  threads,  70 
Table  of  saddle  and  flat  keys,  no 
Table  of  rectangular  sunk  keys,  in 
Table  of  single-riveted  joints,  135 
Table  of  single-riveted  joints,  136 
Table  of  double-riveted  joints,  141 
Table  of  double-riveted  lap-joints,  144 
Table    of  double-riveted    butt-joints, 

147 
Table    of    triple-riveted     butt-joints, 

149 

Table  of  Sellers  clamp  couplings,  174 
Table  of  flanged  shaft  couplings,  180 
Table  of  jaw  clutch  couplings,  183 
Table      of    standard     cast-iron    pipe 

flanges,  192 

Table  of  Pope  pipe  couplings,  196 
Table  of  steam-pipe   connections,  206 
Table  for  brass,  copper,  andwrought- 

iron  pipes,  204 
Table  of  sections,  205 
Table  of  thickness  of  belting,  243,  244 
Table  of  proportions  of  cone  pulleys, 

255 

Table  of  proportion  of  rope  pulleys, 
258,  261 

Table,  Odontagraph,  265,  266 

Table  of  India-rubber  disk  valves, 
290 

Table  of  locomotive-piston  propor- 
tions, 334 

Table  of  thickness  of  pipes,  189 

Table  of  thickness  of  India-rubber 
valve  disks,  283 

Table  of  thickness  of  steam-cylinders^ 
328 

V 

Valve,  Allen-Richardson  balance,  309 
Valve,  American  balance,  310 


INDEX. 


389 


Valve,  Angle  of  advance  of  slide,  307 

Valve,  Ball,  288 

Valve,  Boiler  check,  295 

Valve,  Cocks  and  oil  cup,  278 

Valve  diagram,  The  Bilgram,  313 

Valve  diagram,  The  Zeuner,  320 

Valve,  Flat  India-rubber  disk,  290 

Valve,  foot  and  strainer,  278 

Valve,  Globe,  292 

Valve,  India-rubber,  280 

Valve,  Inside  clearance  of  slide,  308 

Valve,  Lead  of  slide,  307 

Valve,  Overtravel  of  slide,  308 

Valve,  Lift  or  wing,  285 

Valve.  Plain  slide,  305 

Valve,  Point  of  admission  of  slide,  305 

Valve,  Point  of  cut  off  of  slide,  308 

Valve,  Point  of  exhaust  of  slide,  305 


Valve,  Point  of  compression  of  slide, 

305 

Valve,  spindle,  285 
Valve,  stop,  292 
Valve,  Travel  of,  307 

W 

Wall  box  frames,  211 

Wall  brackets,  2id/ 

Wall  or  post  hanger,  223 

Weights  of  cast-iron  water-pipes    42 

Wooden  teeth  or  cogs,  263 

Woods  used  in  construction,  35 

Working  drawings,  17 

Wrist-pin,  370 

Wrought  metals,  33 

Wrought  iron,  Specific  gravity  of,  40 

Wrought-iron  welded  tubes,  44 


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